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Math Help - Find the limit of...

  1. #1
    Junior Member
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    Find the limit of...

    Hi all,

    I am trying to to find the limit of e/ (n + 1) ^(1/2) as n goes to infinity. I can't seem to find any standard limits which will help me. When i graph e/ (n + 1) ^(1/2) it goes to 0... so there must be way to show it

    Thanks in advance,
    ArTiCk
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I am trying to to find the limit of e/ (n + 1) ^(1/2) as n goes to infinity. I can't seem to find any standard limits which will help me. When i graph e/ (n + 1) ^(1/2) it goes to 0... so there must be way to show it

    Thanks in advance,
    ArTiCk
    Note that as n gets significantly large, n+1\sim n.

    So \lim_{n\to\infty}\frac{e}{\sqrt{n+1}}\sim\lim_{n\t  o\infty}\frac{1}{\sqrt{n}}.

    Now as n gets significantly large, \frac{1}{\sqrt{n}} tends to zero.

    Thus, \lim_{n\to\infty}\frac{e}{\sqrt{n+1}}=0.

    Does this make sense?
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