WA 2124 F 16 Hw 20 x WA Larson, Calculus, x Calculus 2 Lectur x G Find the nth M

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WA 2124 F 16 Hw 20 x WA Larson, Calculus, x Calculus 2 Lectur x G Find the nth Mac x G Find the nth Mac x C Chegg Study I Gu x f Online Derivative x C www.webassign.net Assignment-Responses/submit?dep-14318910 /web/Student 2. C+ 20 points LarCalc10 9.8.022. My Notes Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.) (x n 1 (n 1)9 Submit Answer Save Progress 3. 20 points LarCalc10 9.8.026 My Notes Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of enter your answer using interval notation. If the interval of convergence is a finite set enter your answer using set notation.) convergence is an interval, n v2n 1 1) 2n 1 8:53 PM D W e Ask me anything 10/31/2016

Explanation / Answer

2)n=0 to (x-5)n+1/(n+1)9n+1

an=(x-5)n+1/(n+1)9n+1

an+1=(x-5)n+1+1/(n+1+1)9n+1+1

ratio test for convergence:

limn->|an+1/an|<1

limn->|[(x-5)n+1+1/(n+1+1)9n+1+1]/[(x-5)n+1/(n+1)9n+1]|<1

limn->|[(x-5)1/(1+(1/(n+1)))91]|<1

limn->|[(x-5)/(1+(1/(n+1)))9]|<1

|[(x-5)/(1+(0))9]|<1

|(x-5)/9|<1

|x-5|<9

-9<x-5<9

-9+5<x<9+5

-4<x<14

at x=-4 series is n=0 to (-4-5)n+1/(n+1)9n+1=n=0 to (-1)n+1/(n+1) converges by alternating series test

at x=14 series is n=0 to (14-5)n+1/(n+1)9n+1=n=0 to 1/(n+1)  diverges by pseries test ,p=1

interval of convergence is [-4,14)

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