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abb0tBest ResponseYou've already chosen the best response.0
are you being asked to determine whether the power series converges or not?
 8 months ago

RequiemBest ResponseYou've already chosen the best response.0
when simplified i got absolute value of (2x1) Lim n>00 n+1
 8 months ago

abb0tBest 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.
 8 months ago

RequiemBest ResponseYou've already chosen the best response.0
i did that, but not sure if i am right..
 8 months ago

abb0tBest 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.
 8 months ago

abb0tBest ResponseYou've already chosen the best response.0
\[L = \lim_{n \rightarrow \infty}\left \frac{ (n+1)! }{ (2x1)^{n+1} } \times \frac{(2x1)^n}{n!} \right = \lim_{n \rightarrow \infty }\left \frac{ n(n+1)}{ (2x1)(2x1)^n } \ \times \frac{ (2x1)^n }{ n } \right\]
 8 months ago

abb0tBest ResponseYou've already chosen the best response.0
I'm sure you can finish it from here.
 8 months ago

RequiemBest ResponseYou've already chosen the best response.0
so when simplified should be (n+1)(2x1) right?
 8 months ago

RequiemBest 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 ?
 8 months ago

eliassaabBest 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
 8 months ago

RequiemBest ResponseYou've already chosen the best response.0
hey Elias, how did you figure that out?
 8 months ago

eliassaabBest 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.
 8 months ago
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