   Chapter 11.8, Problem 38E

Chapter
Section
Textbook Problem

# If f ( x ) = ∑ n = 0 ∞ c n x n , where cn+4 = cn for all n ≥ 0, find the interval of convergence of the series and a formula for f(x).

To determine

To find: The interval of convergence of the series f(x)=n=0cnxn and formula for f(x) ,where cn+4=cn .

Explanation

Result used:

“The sum of the geometric series with initial term a and common ratio r is n=0arn=a1r where |x|<1 (1)

Calculation:

Express f(x)=n=0cnxn as follows.

n=0cnxn=c0+c1x+c2x2+c3x3+c0x4+c1x5+c2x6+c3x7+=(c0+c1x+c2x2+c3x3)+(c0x4+c1x5+c2x6+c3x7)+=(c0+c1x+c2x2+c3x3)+x4(c0+c1x+c2x2+c3x3)+

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