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lopus Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{n=1}^{\infty} (1)^{n+1}*\frac{ (x1)^n }{ n }\] convergence interval a. (1,1) b.[0,2) c. (0,2] d.[0,2] e.[1,1]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
hmm you are expanding around 1, so disregard answer a and e
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
radius of convergence is 1, so it is one of the middle three your job is to check at the endpoints, and see if it converges at \(x=0\) and if it converges at \(x=2\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
do you know how to do that?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
lets replace \(x\) by 2
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the terms will look like \[(1)^{n+1}\frac{(21)^n}{n}=(1)^{n+1}\frac{1}{n}\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
this is an alternating series, whose terms go to zero, and so when you sum it, it will converge
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
now we repeat the process with \(x=0\) but before we do, is what i wrote above clear?
 2 years ago
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