## anonymous 5 years ago Infinite Series and Factorials question

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

what are you trying to find?

6. anonymous

Sorry - divergence vs convergence test

7. anonymous

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

8. anonymous

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

9. anonymous

Oh right!

10. anonymous

k, got it. Thanks folks.

11. anonymous

you're welcome :)