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Math Help - [SOLVED] convergence of series

  1. #1
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    Question

    How to check if these series converges and how to show it.
    1. (n-7)/(3n^2+5n-6) when n from 1 to infinity
    2.(2^2+6n-7)/(3n^5+5n^3-6) when n goes from 1 to infinity

    Should I use ratio test ?
    Last edited by mr fantastic; December 15th 2008 at 03:34 PM. Reason: Merged the two posts.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by sisa View Post
    How to check if these series converges and how to show it.
    1. (n-7)/(3n^2+5n-6) when n from 1 to infinity
    2.(2^2+6n-7)/(3n^5+5n^3-6) when n goes from 1 to infinity
    Try the limit comparison test, if \sum a_n and \sum bn are infinite series and \lim \frac{a_n}{b_n}=\alpha>0 then the series share convergence/divergence
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  3. #3
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    is for the first case bsubn=1/3n and for the second case bsubb =2/n^3
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  4. #4
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    Quote Originally Posted by sisa View Post
    How to check if these series converges and how to show it.
    1. (n-7)/(3n^2+5n-6) when n from 1 to infinity
    2.(2^2+6n-7)/(3n^5+5n^3-6) when n goes from 1 to infinity

    do you mean

    1. \sum\limits_{n = 1}^\infty {\frac{n-7}{3n^2+5n-6}}

    2. \sum\limits_{n = 1}^\infty {\frac{2n^2+6n-7}{3n^5+5n^3-6}}

    just thought id help with the formatting
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by sisa View Post
    is for the first case bsubn=1/3n and for the second case bsubb =2/n^3
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  6. #6
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    Quote Originally Posted by megamet2000 View Post
    do you mean

    1. \sum\limits_{n = 1}^\infty {\frac{n-7}{3n^2+5n-6}}

    2. \sum\limits_{n = 1}^\infty {\frac{2n^2+6n-7}{3n^5+5n^3-6}}

    just thought id help with the formatting
    yes that is what I mean
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  7. #7
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    Ok.
    I calculated that in cases:
    1.lim an/bn is 1 so since bn diverges to infinity, the series an diverges to infinity
    2.lim an/bn is 1/3 so since bn converges to 1 an also converges to 1

    Right???
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  8. #8
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    Quote Originally Posted by Mathstud28 View Post
    I think I see how you got bn but whats an?
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  9. #9
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    so sisa did you solve this problem? i dont understand how you found the limits..they both look like they would converge to 0.
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