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abb0t Group TitleBest ResponseYou've already chosen the best response.0
are you being asked to determine whether the power series converges or not?
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
when simplified i got absolute value of (2x1) Lim n>00 n+1
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
use ratio test. works about 7580% of the time for most power series. and best test to use when you have factorials.
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
i did that, but not sure if i am right..
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
\[L = \lim_{n \rightarrow \infty}\left \frac{ a_{n+1} }{ a_n } \right\] if L <1 absolutely convergent, and thus convergent L > 1 is divergent L = 1 use different test. but it SHOULD work.
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
\[L = \lim_{n \rightarrow \infty}\left \frac{ (n+1)! }{ (2x1)^{n+1} } \times \frac{(2x1)^n}{n!} \right = \lim_{n \rightarrow \infty }\left \frac{ n(n+1)}{ (2x1)(2x1)^n } \ \times \frac{ (2x1)^n }{ n } \right\]
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
I'm sure you can finish it from here.
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
so when simplified should be (n+1)(2x1) right?
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
so i pull the 2x1 out and im left with the Lim n>00 of n+1 ?
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
thanks abbot!!
 one year ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.0
Your series diverges everywhere except for x =1/2. You can do it by the divergence test, the nth terms does not go to zero, then the series diverges
 one year ago

Requiem Group TitleBest ResponseYou've already chosen the best response.0
hey Elias, how did you figure that out?
 one year ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.0
It is a power series. if \( x\ne \frac 1 2\), then n!(2x1)^n goes to infinity with n, so the nthterm does not go to zero, so the series is divergent.
 one year ago
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