# Representing functions by power series | Ch 9.4 - 52E

## Problem 52E Chapter 9.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 52E

Representing functions by power series Identify the functions represented by the following power series.

Step-by-Step Solution:

Solution 52E

Step 1:

In this problem we need to identify the function represented by the power series .

Consider ,  = ++++.........

= ++++..........  Is  an infinite geometric series , here “ first term (a) = x , common ratio (r)= =

 We know that  a+ar+                                 Then () = , if  |r|< 1 ,  , if |r| > 1

Therefore , ++++..........  is  an infinite geometric series, then

=  = f(x) .

Therefore , the function f(x) =  represented by the power series .

Step 2 of 2

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Representing functions by power series | Ch 9.4 - 52E

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