Chapter 9.8, Problem 81E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Proof For n > 0 , let R > 0 and c n > 0 . Prove that if the interval of convergence of the series ∑ n = p ∞ c n ( x − x 0 ) n is ⌊ x n − R  \$ x 0 + R ⌋ , then the series converges conditionally at x = x 0 − R

To determine

To Proof: The given series n=0cn(xx0)n  converges conditionally at x=x0R if the interval of convergence of the series is [x0R, x0+R]

Explanation

Given: n=0cn(xx0)n , n0,R0,cn0

Proof:

The given series is n=0cn(xx0)n and interval of convergence is [x0R, x0+R]At the point x.0+R, n=0cn(xx0)n=n=0cnRn , DivergesAt the point x0

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