Convergence of Sequence: (n^2)/(e^n)

[k_squared]

NEVERMIND! IT IS 0! I SOMEHOW WAS STARING AT THE WRONG ANSWER SHEET FOR A LITTLE BIT! THANK YOU!

1. Homework Statement

Determinte whether the sequence converges or diverges:
(n^2)/(e^n)2. Homework Equations

The book says that the solution is: e/(e-1).

However, the limit of the equation y=(n^2)/(e^n) as n goes to infinity is 0.

I don't know why I can't seem to apply the theorem that:

If the limit as x goes to infinity of f(x) = L and f(n)= a_n, then the limit of a_n as x approaches infinity is L.

3. The Attempt at a Solution

I used L'Hôpital's rule to prove the limit is 0. Wolfram alpha confirms this.

 

[LCKurtz]

The question is whether the sequence converges, so the answer would be yes or no, right? What question does your book say e/(e-1) is the answer to? You are correct that the sequence converges to 0. Have you stated the question fully?