Proving Convergence of Two Sums at 0

[tbone413]

Homework Statement

Prove that the following sums only converge at 0.
sum of: e^(n^2)*x^n , and
sum of: e*n^(n)*x^(n)

Homework Equations

well i know series converge if the lim as n approaches inf of the abs(x-c) is less than (An/An+1) but I have no idea how to prove it, I saw these for the first time yesterday in class, and don't know much about it.

The Attempt at a Solution

 

[HallsofIvy]

Whart you are talking about is the "ratio test" for power series. What is A_n+1/A_n for these series?

 

[dynamicsolo]

Homework Statement

Prove that the following sums only converge at 0.
sum of: e^(n^2)*x^n , and
sum of: e*n^(n)*x^(n)

Are you missing either division signs or negative signs in exponents somewhere? I don't see how these are going to converge to zero as you've written them...

 

[HallsofIvy]

Are you missing either division signs or negative signs in exponents somewhere? I don't see how these are going to converge to zero as you've written them...

He didn't say they converge to 0, he said they only converge at x= 0.

 

[dynamicsolo]

He didn't say they converge to 0, he said they only converge at x= 0.

Sorry, missed the 'only'; I've read too many sentences with wrong prepositions lately and thought the OP meant 'to'. (Your mentioning the Ratio Test reinforced this...)

The first question might be: how do you write the power series for these exponential functions? What do you get when you multiply them by x^n?