Which of the following describes the sequence a_n = (-1)^n \cdot \frac{n}{n+1} ?

The sequence is divergent because it oscillates between two different values.

Convergent and divergent sequences

Divergent and Convergent Thinking and The Design Thinking Process Warm-Ups 10/27&28/25

Plate tectonic theory, Divergent and convergent, continental drift theory, seafloor spreading theory

Lesson 2: Plate Tectonics There are a few handfuls of major plates and dozens of smaller, or minor, plates. Six of the majors are named for the continents embedded within them, such as the North American, African, and Antarctic plates. Though smaller in size, the minors are no less important when it comes to shaping the Earth. The tiny Juan de Fuca plate is largely responsible for the volcanoes that dot the Pacific Northwest of the United States. The plates make up Earth's outer shell, called the lithosphere. (This includes the crust and uppermost part of the mantle.) Churning currents in the molten rocks below propel them along like a jumble of conveyor belts in disrepair. Most geologic activity stems from the interplay where the plates meet or divide. The movement of the plates creates three types of tectonic boundaries: convergent, where plates move into one another; divergent, where plates move apart; and transform, where plates move sideways in relation to each other. They move at a rate of one to two inches (three to five centimeters) per year. Convergent BoundariesWhere plates serving landmasses collide, the crust crumples and buckles into mountain ranges. India and Asia crashed about 55 million years ago, slowly giving rise to the Himalaya, the highest mountain system on Earth. As the mash-up continues, the mountains get higher. Mount Everest, the highest point on Earth, may be a tiny bit taller tomorrow than it is today. These convergent boundaries also occur where a plate of ocean dives, in a process called subduction, under a landmass. As the overlying plate lifts up, it also forms mountain ranges. In addition, the diving plate melts and is often spewed out in volcanic eruptions such as those that formed some of the mountains in the Andes of South America. At ocean-ocean convergences, one plate usually dives beneath the other, forming deep trenches like the Mariana Trench in the North Pacific Ocean, the deepest point on Earth. These types of collisions can also lead to underwater volcanoes that eventually build up into island arcs like Japan. Divergent Boundaries At divergent boundaries in the oceans, magma from deep in the Earth's mantle rises toward the surface and pushes apart two or more plates. Mountains and volcanoes rise along the seam. The process renews the ocean floor and widens the giant basins. A single mid-ocean ridge system connects the world's oceans, making the ridge the longest mountain range in the world. On land, giant troughs such as the Great Rift Valley in Africa form where plates are tugged apart. If the plates there continue to diverge, millions of years from now eastern Africa will split from the continent to form a new landmass. A mid-ocean ridge would then mark the boundary between the plates. Transform Boundaries The San Andreas Fault in California is an example of a transform boundary, where two plates grind past each other along what are called strike-slip faults. These boundaries don't produce spectacular features like mountains or oceans, but the halting motion often triggers large earthquakes, such as the 1906 one that devastated San Francisco.

Pressure, or decompression, enables the mantle rock to melt and form magma. Decompression melting often occurs at divergent boundaries, where tectonic plates separate. The rifting movement causes the buoyant magma below to rise and fill the space of lower pressure. The rock then cools into new crust. Decompression melting also occurs at mantle plumes, columns of hot rock that rise from Earth's high-pressure core to its lower-pressure crust. When located beneath the ocean, these plumes, also known as hot spots, push magma onto the seafloor. These volcanic mounds can grow into volcanic islands over millions of years of activity. Transfer of Heat Magma can also be created when hot, liquid rock intrudes into Earth's cold crust. As the liquid rock solidifies, it loses its heat to the surrounding crust. Much like hot fudge being poured over cold ice cream, this transfer of heat is able to melt the surrounding rock (the "ice cream") into magma. Transfer of heat often happens at convergent boundaries, where tectonic plates are crashing together. As the denser tectonic plate subducts, or sinks below, or the less-dense tectonic plate, hot rock from below can intrude into the cooler plate above. This process transfers heat and creates magma. Over millions of years, the magma in this subduction zone can create a series of active volcanoes known as a volcanic arc. Flux Melting Flux melting occurs when water or carbon dioxide are added to rock. These compounds cause the rock to melt at lower temperatures. This creates magma in places where it originally maintained a solid structure. Much like heat transfer, flux melting also occurs around subduction zones. In this case, water overlying the

Continental Drift Theory. From the discussion of the rock cycle, it has been pointed out that through Earth's external and internal processes. Earth's surface is constantly changing. However, this idea of a changing environment did not conform with the belief of earlier scientists. Rather, they thought that the geographic positions of ocean basins and continents have been static since the beginning of time. It was around the 1500s when Leonardo da Vinci, upon his discovery of fossil seashells found at the high mountains of Italy, first thought of the idea that the areas where mountains are located may have been oceans in the past. Through time, other fossils of marine organisms found far above the current sea level further supported the idea that mountains were uplifted and weathering wore them down. At around the 1800s, most scientists have accepted the idea that Earth's crust is undergoing large vertical movements or uplifting. There was also evidence of possible horizontal movements, but the scientists then were not convinced about it. Alfred Wegener showed evidence of horizontal or lateral movement of the continents in his continental drift theory. According to him, the continents have drifted around the world and have once formed a giant landmass or supercontinent called Pangaea. To support his theory, Alfred Wegener presented a set of geographical, biological, and climatic evidence.Wegener's geographical evidence included the jigsaw puzzle fit of the current continents. He pointed out that the coastlines of South America and Africa seem to fit together. He also pointed the presence of mountain ranges having similar rock types and age but separated by vast oceans, like that of the folded rocks of the Caledonian mountains. The same folded rocks run through West Africa, North America, Newfoundland, Ireland, Wales, Scotland, Greenland, and Norway, all of which are now separated by the Atlantic Ocean. A geographical evidence on the similar rock types in West Africa, North America, Greenland, and Europe is found. The biological evidence came in the discovery of similar plant and animal fossils in different continents separated by oceans. The animal fossils of Mesosaurus and Lystrosaurus indicate that they were not capable of crossing the oceans to reach the other continents. If they were, the fossils should have been more widely distributed Africa, Australia, India, and South America were too large to be carried by wind. This indicates that the areas where the fossils were found were closely linked. It has also been found out that the plant only grew in areas with subpolar climate, which would indicate that the landmasses were located near the South Pole.Lastly, for his climatic evidence, Wegener discovered that a glacial period occurred during the late Paleozoic era in Southern Africa, South America, Australia, and India. The initial explanation for this event was global cooling, but it was rejected because large tropical swamps with so much vegetation were found at the same time in the Northern Hemisphere. This further supported the idea that the supercontinent was indeed near the South Pole, and the continents in Northern Hemisphere were once near the equator. The glacial period also left glacial striations, or the scratches glaciers make as they move across on the underlying bedrock, on the aforementioned continents. For such an event to happen, the continents would have to be connected. SCIENCE PIONEER. Alfred Wegener (1880-1930). Alfred Wegener was a German polar researcher, geophysicist, and meteorologist. He was known for his work on the continental drift theory. In his effort to defend his work, he went to the Greenland ice sheet where he died.Even with all the compelling evidence, the continental drift theory hardly convinced the scientific community at that time because Wegener was unable to identify a credible mechanism that drives the continental drift. He was unable to clearly explain how the continents moved and how the larger continents broke through the ocean floor. Eventually, critics of the continental drift began to accept the theory when new evidence supporting the theory was discovered. The new evidence led to a more encompassing theory the theory of plate tectonics. This theory provided a more convincing explanation as to how the continents moved. The evidence that paved the way for the theory of plate tectonics was the idea of wandering poles. Scientists began studying volcanic rocks to determine the location of the magnetic poles. When volcanic rocks crystallize, the minerals with magnetic properties align themselves parallel to Earth's magnetic field at the time the minerals were formed. This finding allowed scientists to determine the polarity of Earth's magnetic field and the magnetic inclination that showed the location of the poles. Upon studying the paleomagnetism of the rocks, geophysicists found out that rocks from various locations point to different magnetic north poles, suggesting that the poles have wandered. Since movement of magnetic poles is very unlikely, scientists have accepted the idea that the continents are indeed moving. And if the continents are moving, scientists thought that maybe the ocean basins are moving too. They also discovered that some rocks showed magnetic reversals, which led them to believe that the magnetic north pole now was not always the magnetic north pole. Seafloor Spreading. After World War II, exploration on the ocean floor became the focus of many geologic studies. It was only then that the ocean ridge system was discovered. A geologist in Princeton University named Harry Hess, along with other scientists, studied this ocean ridge system and hypothesized that the oceanic crust was moving away from the ridge. His hypothesis, known as seafloor spreading, showed that the ocean floor is split along the ridge where the magma rises to form the new ocean floor.Because of this, rocks located near the ridge are younger than those that are located magnetic polarity of Earth is also preserved in those rocks. Withe ridge scientists were able to see the magnetic reversals in the ocean floor, and they were able to make use of information to determine that the ocean floor is moving at a rate of about 10 cm per year. Plate Tectonics. Confirmation of the seafloor spreading hypothesis proved that continents are not moving above the ocean floor. Rather, it is the fragments of the lithosphere. The lithosphere is the rigid layer that is composed of the uppermost mantle and the crust that carry the continents and the ocean basins along. These fragments of the lithosphere are called plates. Underneath the lithosphere is a weaker region in the mantle known as asthenosphere that behaves like a fluid. Thus, the lithosphere floats above the asthenosphere, making it detached and free to move. This became the basis of the theory of plate tectonics. Now that it has been made clear that it is the plates which are moving, the question as to how they move remained. Sir Arthur Holmes proposed the driving force for this plate movement in 1919. He suggested that the movement in the mantle carries the plates along. It was previously discussed that Earth's interior is very hot due to the heat produced by radioactive decay. Convection takes place in the mantle, keeping the asthenosphere hot and weak. The convection currents produced in the asthenosphere are the ones carrying the lithospheric plates and making them move. However, convection currents are not enough. Mechanisms such as ridge push and slab pull aid the convection currents to slowly move the lithospheric plates. Ridge push occurs at mid ocean ridges which are higher in elevation than the surrounding trenches and abyssal plains. The new ocean floor from the ridge is hot and relatively thin. As it moves away from the ridge, it cools down and gets denser, heavier, and thicker. Below this cooling ocean floor is the asthenosphere, which is less dense. This area becomes a massive shear zone and the new ocean floor will effectively slide down the slope of the asthenosphere. When the plate collides with another plate with lesser density, the denser plate sinks and a subduction zone is formed. When the subducting plate sinks, it pulls on the rest of the plate behind it. These mechanisms explain the movement of the plates.Earth has seven major lithospheric plates that account for 94% of Earth's surface. These are the North American Plate, South American Plate, Pacific Plate, African Plate, Eurasian Plate, Indo-Australian Plate, and Antarctic Plate. These plates are constantly moving relative to the other plates. Thus, the interaction of plates occurs mostly along the boundaries. These movements are plotted using information from earthquakes and volcanic activities. There are three main types of plate boundaries: convergent, divergent, and transform boundaries Convergent boundaries are boundaries where two plates move towards each other A convergent boundary is also known as destructive margin since this is where the collision between two plates occhins. There are three types of convergence-oceanic oceanic, oceanic-continental, and continental-continental. Trenches are features of the ocean floor that are present in both oceanic-oceanic boundary and oceanic-continental boundary. Subduction occurs at the trenches, therefore, these are characterized as the deepest parts of Earth. A divergent boundary is the opposite of convergent boundary: two plates move away from each other. Divergent boundaries create new crust; thus, they are also known as constructive margins. The ocean ridge system is a divergent boundary where new ocean floor is produced as magma rises, pushing the older rocks aside.Transform boundary is also known as conservative plate margin since two plates just move past one another, neither creating nor destroying land. Earthquake epicenters are usually detected at transform boundaries because the rocks tend to break and not fold or sink, like in convergent boundaries. Evolution of the Ocean Basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins.Continents do not immediately end at the point where the ocean meets the land. They may extend slightly into the oceans. The portion of the continent that is submerged is called continental margin. There are two types of continental margin: passive margin and active margin. A passive continental margin consists of a continental shelf, continental slope, and continental rise. It is not associated with plate boundaries; thus, there are very little tectonic activities. An active continental margin only has a continental shelf and a continental slope. It is associated with plate boundaries; thus, a main feature of this boundary is a trench. The different features of a continental margin are the following: 1. The continental shelf is the gently-sloping submerged portion of the continent. 2. The continental slope is the steep slope after the continental shelf. It is still part of the continent. 3. The continental rise is the gently-sloping area after the continental slope and before the ocean floor. 4. The trenches are the deepest parts of the ocean. These are narrow depressions caused by the subduction of the ocean floor along the convergent boundaries. 5. The mid-oceanic ridge is the mountain range system in the ocean. It is responsible for the production of new ocean floor. This is the region where new magma constantly emerges from. SCIENCE CAREER. A scientific illustrator uses art to inform and communicate complex details and concepts of science. He/She makes use of scientifically informed observations and research along with his/her technical art and aesthetic skills to make accurate representations. In Natural History, the scientific illustrators recreate how the extinct species look like by working with scientists and fossil records. Moreover, with the advances in technology, illustrators are now into 3D modelling, animation, and video making. Earth's History. All the processes that have been discussed require long periods of time to create a noticeable change on Earth's surface. You can just imagine how long it would take to create an oceanas vast as the Pacific Ocean if the ocean floor moves only at about 10 cm/year. It is then important to know the history of Earth to learn the complexities of its past and be able to use it to understand the present. Just like learning the history of a country that requires one to read a lot of books, learning the history of Earth involves studying a lot of rocks. Rocks, especially sedimentary rocks, contain a lot of information about Earth's past. It holds the key to most of the geologic processes that happened on Earth and the key to uncovering how life on Earth evolved. But these discoveries are worthless if there is no time perspective. Thus, one of the most important contributions of geologists to mankind is the geologic time scale, which holds a history that is exceedingly long.

Virtual images from converging and diverging lenses

One of the worst things about living in a city is the high cost of living. Pros and Cons of Living in a City Living in a city offers numerous advantages, but it also comes with its own set of drawbacks. Here are the pros and cons of living in a city: Pros: Job Opportunities: Cities are often hubs for various industries and businesses, providing a wide array of job opportunities across different sectors. This can lead to better career prospects and higher earning potential for residents. Cultural Diversity: Cities are melting pots of different cultures, traditions, and lifestyles. This diversity enriches the social fabric of the city, offering exposure to various cuisines, arts, festivals, and languages. Access to Amenities: Cities typically offer an abundance of amenities such as restaurants, shopping centers, entertainment venues, healthcare facilities, educational institutions, and public services. Residents have easy access to these conveniences. Public Transportation: Many cities have well-developed public transportation systems, including buses, subways, trains, and trams. This can make commuting more convenient and reduce the need for personal vehicles. Entertainment and Recreation: Cities are known for their vibrant nightlife, cultural events, museums, theaters, sports venues, and recreational spaces. Residents can enjoy a wide range of entertainment options. Educational Opportunities: Cities often boast prestigious universities, colleges, and research institutions. This provides residents with access to quality education and lifelong learning opportunities. Healthcare Facilities: Major cities tend to have top-tier medical facilities and specialized healthcare services, ensuring that residents have access to advanced healthcare resources. Cons: Cost of Living: Cities are often associated with a higher cost of living due to expensive housing, transportation expenses, dining out costs, and other daily expenses. Noise and Pollution: Urban areas can be noisy and polluted due to heavy traffic, industrial activities, construction projects, and densely populated neighborhoods. Crowded Environment: Cities are densely populated, leading to crowded streets, public spaces, and public transportation systems. This can result in congestion and longer commute times. Limited Green Spaces: While cities offer many amenities, they may lack sufficient green spaces such as parks or gardens for residents to relax and connect with nature. Stressful Lifestyle: The fast-paced lifestyle in cities can contribute to higher stress levels for some individuals due to demanding work environments and busy schedules. Security Concerns: Certain urban areas may face higher crime rates compared to rural or suburban areas, leading to concerns about safety and security. Traffic Congestion: Heavy traffic congestion is a common issue in cities, leading to longer commute times and frustration for residents who rely on personal vehicles or public transportation. In conclusion, living in a city presents both advantages and disadvantages that individuals should carefully consider based on their lifestyle preferences and priorities.

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