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Find the Maclaurin series for the functions.$$5 \cos \pi x$$

$$5-\frac{5 \pi^{2} x^{2}}{2 !}+\frac{5 \pi^{4} x^{4}}{4 !}-\frac{5 \pi^{6} x^{6}}{6 !}+\dots$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

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Lectures

01:59

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.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

01:26

Find the Maclaurin series …

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Use the Maclaurin series f…

07:47

For the maclaren series of the function 5 times cosine of pi times x, so first we used the result to make or series of the function. Cosine of x is equal to sum, and from 0 to infinity negative 1 to the power of n times x. To the power of 2 n over 2 n factorial, then replace x by pi times x and then multiply 5. We get clar series of the function 5 times. Cosine of pi x is equal to sum, and from 0 to infinity 5 pints negative 12 n times. Pi to the power times x to the power 2 n over 2 n actori.

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