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Limit of a Sequence

  1. Jan 23, 2014 #1
    Hello again,

    I am having trouble with a particular limit problem and would appreciate any help/pointers you can offer. The question is asking for the nth term of the sequence [tex]2, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}[/tex]

    .. and also asks for a limit of the sequence. My immediate guess was to apply l'hopital's rule, which would mean setting n to approach infinity and using something like this:

    [tex]lim_n→∞ \frac{n+1}{n}[/tex]

    It seems to me like it could work, however I do not understand how an actual 'limit' value can be determined from a sequence of unknown and changing numbers ('n'). What I mean is, in order to make my limit work then the nth term would have to equal infinity, would it not?

    ** Edit **: According to an online limit solver the limit is 1, which I can see is possible if the n values are cancelled out.
     
  2. jcsd
  3. Jan 23, 2014 #2

    LCKurtz

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    You don't "cancel out" the ##n##'s. You write as$$
    \frac{n+1} n = \frac n n + \frac 1 n = 1 + \frac 1 n$$and take the limit as ##n\to\infty## of that.
     
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