Determine the interval of convergence for

[Jamin2112]

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 n^th 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?

 

[D H]

Correct.