Taking the Limit As N -> Infinity

[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

 

[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.

 

[student45]

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

 

[BSMSMSTMSPHD]

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

 

[student45]

Doh! Thanks. Got it.