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Math Help - does this series converge?

  1. #1
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    does this series converge?

    \sum {\frac {2+sin^3(n+1)} {2^n + n^2} }

    Can someone show me this plz?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cato View Post
    \sum {\frac {2+sin^3(n+1)} {2^n + n^2} }

    Can someone show me this plz?
    note that \Bigg| \frac {2 + \sin^3 (n + 1)}{2^n + n^2} \Bigg| \le \Bigg| \frac {2 + 1}{2^n + n^2} \Bigg| = \Bigg| \frac 3{2^n + n^2} \Bigg|

    now what can you say?
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  3. #3
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    \Bigg| \frac 3{2^n + n^2} \Bigg| < \Bigg| \frac 3{n^2} \Bigg| which we know converges so the whole thing converges, right?
    Last edited by Cato; October 9th 2008 at 11:17 PM.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cato View Post
    \Bigg| \frac 3{2^n + n^2} \Bigg| < \Bigg| \frac 3{n^2} \Bigg| which we know converges so the whole thing converges, right?
    yes, it converges absolutely by the comparison test. and absolute convergence implies convergence
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