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anonymous
 5 years ago
Power Series: sigma n=1 n> infinity ((n(n+1)^n)/4^n) so far ive gotten IxI < (1/4) how do i find the interval of convergence and radius of convergence?
anonymous
 5 years ago
Power Series: sigma n=1 n> infinity ((n(n+1)^n)/4^n) so far ive gotten IxI < (1/4) how do i find the interval of convergence and radius of convergence?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you dont have x in your summation, how can you get x < 1/4?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0woops sigma n=1 n> infinity ((n(x+1)^n)/4^n) IxI < (1/4)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by using the root test, you will get the limit (n^(1/n))[(x+1)/4]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since lim (n^(1/n)) = 1, for the series to converge, you get x+1 < 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh okay hmm okay now how would I find the intervals of convergence?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the radius of convergence is 4, and it is around 1. So the interval we are interested is (5,3)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay so we plug in what makes it zero which in this case is 1, and how did you get the interval?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by solving x+1 < 4. 4 < x+1 < 4 5 < x < 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So check the convergence of the series at the end points

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how would I know to apply the root test? ratio?
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