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lopusBest 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]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
hmm you are expanding around 1, so disregard answer a and e
 one year ago

satellite73Best 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 \(x=2\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
do you know how to do that?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
lets replace \(x\) by 2
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the terms will look like \[(1)^{n+1}\frac{(21)^n}{n}=(1)^{n+1}\frac{1}{n}\]
 one year ago

satellite73Best 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
 one year ago

satellite73Best 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?
 one year ago
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