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Requiem
 one year ago
Power series problem:
n!(2x1)^n
from 1 to infinity
Requiem
 one year ago
Power series problem: n!(2x1)^n from 1 to infinity

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

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

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

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

abb0t
 one year ago
Best 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.

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

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

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

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

eliassaab
 one year ago
Best ResponseYou've already chosen the best response.0Your 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

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

eliassaab
 one year ago
Best ResponseYou've already chosen the best response.0It 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.
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