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Problem

List the first five terms of the sequence. $ a_n…

01:49

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Problem 6 Easy Difficulty

List the first five terms of the sequence.
$$ a_n = \cos {n \pi}{2} $$

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

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Lectures

01:59

Series - Intro

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

Sequences - Intro

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

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Video Transcript

for any pulls. One. We have coastline of two pi, which is one for any calls to you have co sign of two times two pie no co signed for pie. But co sign has a period of two pi, which means that we can add or subtract any multiple of two pi from co sign and get the same thing. So this is the same thing as co sign of two pi. That's just one can is gonna be the same thing for any equals three and equals foreign and equals five first five terms in our sequence should be one on one, one on one. Okay, we should be able to see that we're going to get the same thing, because regardless of what value of n we have plugged in here as long as it's the whole number, it's just going to give us some multiple of two pi and again, since coastline as period to pie, we can just add or subtract any multiple of two pi and it'LL just give us the exact same answer

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