   Chapter 11.R, Problem 30E

Chapter
Section
Textbook Problem

Find the sum of the series. ∑ n = 0 ∞ ( − 1 ) n π n 3 2 n ( 2 n ) !

To determine

To find

The sum of the series

Explanation

1) Concept:

Use Taylor series of cosx  to find the sum of the given series.

2) Formula:

Taylor series of cosx  is

cosx= n=0-1nx2n(2n)!

2) Calculations:

Consider

n=0-1nπn32n2n!

It can be rearranged as

n=0-1n12n

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