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lopus
 3 years ago
power serie
lopus
 3 years ago
power serie

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lopus
 3 years ago
Best 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]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0hmm you are expanding around 1, so disregard answer a and e

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0radius 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 \(x=2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0do you know how to do that?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0lets replace \(x\) by 2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the terms will look like \[(1)^{n+1}\frac{(21)^n}{n}=(1)^{n+1}\frac{1}{n}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0this is an alternating series, whose terms go to zero, and so when you sum it, it will converge

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