   Chapter 11.10, Problem 1E

Chapter
Section
Textbook Problem

# If f ( x ) = ∑ n = 0 ∞ b n ( x − 5 ) n for all x, write a formula for b8.

To determine

To write: The formula for b8 .

Explanation

Given:

The function is f(x)=n=0bn(x5)n for all x.

Theorem used:

"If f has a power series representation at a, which can be written as f(x)=n=0cn(xa)n    |xa|<R , then its coefficient are given by the formula cn=f(n)(a)n! .

Calculation:

Consider the given function f(x)=n=0bn(x5)n

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