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lopus
 2 years ago
power serie
lopus
 2 years ago
power serie

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lopus
 2 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]

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1radius 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 \(x=2\)

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

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

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

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

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