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Math Help - [SOLVED] Sum of infinite series

  1. #1
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    [SOLVED] Sum of infinite series

    Determine whether the given infinite series converges or diverges. If it converges, find its sum.

    <br />
\sum_{n=1}^{\infty}\frac{2n}{\sqrt{4n^2+3}}<br />

    Any help is greatly appreciated!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    You should try to take 4n^2 out of the square root to find the limit of \frac{2n}{\sqrt{4n^2+3}} when n\to \infty.
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Hi

    You should try to take 4n^2 out of the square root to find the limit of \frac{2n}{\sqrt{4n^2+3}} when n\to \infty.
    How do I take 4n^2 out of the square root?
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  4. #4
    Super Member flyingsquirrel's Avatar
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    You can factor 4n^2 : \sqrt{4n^2+3}=\sqrt{4n^2\left(1+\frac{3}{4n^2}\rig  ht)}<br />
=\sqrt{4n^2}\sqrt{1+\frac{3}{4n^2}}=\ldots
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  5. #5
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    Quote Originally Posted by flyingsquirrel View Post
    You can factor 4n^2 : \sqrt{4n^2+3}=\sqrt{4n^2\left(1+\frac{3}{4n^2}\rig  ht)}<br />
=\sqrt{4n^2}\sqrt{1+\frac{3}{4n^2}}=\ldots

    I see what I need to do now. Thank you!
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