   Chapter 11.9, Problem 7E

Chapter
Section
Textbook Problem

# Find a power series representation for the function and determine the interval of convergence.7. f ( x ) = x 2 x 4 + 16

To determine

To find: The power series representation for the function f(x)=x2x4+16 and determine the interval of convergence

Explanation

Result used:

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

Calculation:

Consider f(x)=x2x4+16

Divide the numerator and the denominator by 16

x2x4+16=x216x416+1616=x2161+x416=x2161(x416)

Compare to equation (1), the given function f(x) is a sum of a geometric series with initial term a=x216 and common ratio r=x416 .

That is, x2161(x416)=n=0(x216)(x416)n

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