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Taking the Limit As N -> Infinity

  1. Nov 27, 2006 #1
    Taking the Limit As N --> Infinity

    [tex]\mathop {\lim }\limits_{n \to \infty } \frac{{n^n x}}{{(n + 1)^n }}[/tex]

    Does this limit exist? Somehow it's supposed to come down to x/e
     
    Last edited by a moderator: Nov 27, 2006
  2. jcsd
  3. Nov 27, 2006 #2
    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.
     
  4. Nov 27, 2006 #3
    Got everything except the magic... the goal is to get (1+(1/n))^n, right?
     
  5. Nov 27, 2006 #4
    Well, that would be e. You want 1/e.
     
  6. Nov 27, 2006 #5
    Doh! Thanks. Got it.
     
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