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Math Help - Need help with a serie

  1. #1
    Member javax's Avatar
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    Arrow Need help with a serie

    Supp guys...I've got a serie I don't know how to find its limit, nor the sum!
    If you could help me I would appreciate!
    Here it is:
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  2. #2
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    Quote Originally Posted by javax View Post
    Supp guys...I've got a serie I don't know how to find its limit, nor the sum!
    If you could help me I would appreciate!
    Here it is:
    As with all series, you should start by asking yourself approximately how large is the n'th term of the series. In this case, for large values of n, \frac{\sqrt n+1}{\sqrt[3]{n^5}} is approximately \frac{n^{1/2}}{n^{3/5}} = n^{-1/10}. Then \textstyle 1-\cos(n^{-1/10})\approx \frac12n^{-1/5} (from the power series expansion of cos). So the series diverges, by comparison with \textstyle\sum n^{-1/5}.
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