Homework Help: Taking the Limit As N -> Infinity

1. Nov 27, 2006

student45

Taking the Limit As N --> Infinity

$$\mathop {\lim }\limits_{n \to \infty } \frac{{n^n x}}{{(n + 1)^n }}$$

Does this limit exist? Somehow it's supposed to come down to x/e

Last edited by a moderator: Nov 27, 2006
2. Nov 27, 2006

BSMSMSTMSPHD

Factor out the x (the limit is with respect to n).

Consolidate the remaining factors into a term with a single exponent.

Perform a little magic inside the parentheses and look for something familiar.

3. Nov 27, 2006

student45

Got everything except the magic... the goal is to get (1+(1/n))^n, right?

4. Nov 27, 2006

BSMSMSTMSPHD

Well, that would be e. You want 1/e.

5. Nov 27, 2006

student45

Doh! Thanks. Got it.