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Math Help - Limit

  1. #1
    Senior Member pankaj's Avatar
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    Limit

    Evaluate:
    <br />
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}})
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by pankaj View Post
    Evaluate:
    <br />
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}})
    As each of the denominators get larger and larger, we see that each of those terms approach zero.

    So, <br />
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}}) = 0+0+0+\dots+0=\color{red}\boxed{0}

    Does this make sense?

    --Chris
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  3. #3
    Senior Member pankaj's Avatar
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    Answer is given as 2.
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