Question

Infinite Series and Factorials question

Answer 1

Hey so there's this question in my textbook: \[\sum_{n=1}^{\infty} (2n!*x^n)/n!\]

Answer 2

I was thinking I could simplify it by writing 2n! = 2^n*n!. Is this possible?

Answer 3

Because (2n)! = 2*4*6*8..(2n)

Answer 4

Sorry I meant to type (2n)! instead of 2n!

Answer 5

what are you trying to find?

Answer 6

Sorry - divergence vs convergence test

Answer 7

ah use the ratio test. then it doesnt matter if it simplifies

Answer 8

that's wrong! because (2n)!=(2n)*(2n-1)*(2n-2)...3*2*1

Answer 9

Oh right!

Answer 10

k, got it. Thanks folks.

Answer 11

you're welcome :)