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Σ Consider the power series. (-3)^(x-2)^. √n+2 n=o 5 1. Use Limit Comparison Test to show that the series diverges when x=-=-=-

Σ Consider the power series. (-3)^(x-2)^. √n+2 n=o 5 1. Use Limit Comparison Test to show that the series diverges when x=-=-=-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please show step by step solution on how to get the circled part with complete explanation. do this typewritten and i will upvote. skip if you already did this

(-3)^(x-2)^ Consider the power series. √n+2 n=o 1. Use Limit Comparison Test to show that the series diverges when x=-=- X= x = 3: (-3)^(x-2)^ √n+2 (-3)^(-2)^ = √n+2 (-3)^(-1)^ √n +2 at x = n=0 348 ⇒diverges lim 1 > 0 - 13/12 Now, the series is divergent at x = - Since an diverges, therefore by Limit Comparison Test, bn also diverges. = عالم Now, bn = n Hence, an <bn Using Limit Comparison Test √√n+2 lim an lim 0+2 = n+f bo = 10 no √n+2 √nt2 n+ 2 n=o lim n+ (1) √n+2 nt 2
Transcribed Image Text:(-3)^(x-2)^ Consider the power series. √n+2 n=o 1. Use Limit Comparison Test to show that the series diverges when x=-=- X= x = 3: (-3)^(x-2)^ √n+2 (-3)^(-2)^ = √n+2 (-3)^(-1)^ √n +2 at x = n=0 348 ⇒diverges lim 1 > 0 - 13/12 Now, the series is divergent at x = - Since an diverges, therefore by Limit Comparison Test, bn also diverges. = عالم Now, bn = n Hence, an <bn Using Limit Comparison Test √√n+2 lim an lim 0+2 = n+f bo = 10 no √n+2 √nt2 n+ 2 n=o lim n+ (1) √n+2 nt 2
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