- #1
Jamin2112
- 986
- 12
Homework Statement
[n=0 to ∞] ∑x2n/n!
Homework Equations
The ratio test
The Attempt at a Solution
So, here is the ratio of of the (n+1)th term to the nth term:
| [x2(n+1)/(n+1)!] / [x2n/n!] | =
| [x2nx2/(n+1)!] * [n!/x2n] | =
| x2/n |, which will be will be less than one when n is big enough.
So this converges for all x, right?