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ertagon2
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Could someone check if my answers are right and help me with question 5?
View attachment 8055
View attachment 8055
A sequence is a list of numbers that follow a specific pattern or rule. The numbers in a sequence are usually denoted by a subscript and are written in a specific order.
The limit of a sequence is the value that the terms in the sequence approach as the number of terms increases towards infinity. This means that as the terms in the sequence get closer and closer to the limit, the difference between them becomes smaller and smaller.
A sequence converges if its terms approach a finite value (the limit) as the number of terms increases towards infinity. On the other hand, a sequence diverges if its terms do not approach a finite value and instead either increase or decrease without bound.
The supremum of a sequence is the smallest number that is greater than or equal to all of the numbers in the sequence. In other words, it is the upper bound of the sequence.
Sequences are used in various areas of science, such as physics, engineering, and computer science, to model and analyze real-world phenomena. For example, the Fibonacci sequence is used to describe the growth of populations in biology, while the harmonic sequence is used to analyze the vibrations of musical instruments in physics.