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Math Help - taylor series power question..

  1. #1
    MHF Contributor
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    taylor series power question..

    when i develop the series of a cosine i have a (-1) member
    i wanted to represent the series as a sum
    so i need to take only the odd members so the power of -1 is 2k+1 i got
    but the solution says that the power of -1 is equal (-1)^{k-1}

    is it the same??
    why they have such an expression
    (they use n istead of k)
    http://i45.tinypic.com/6sszue.jpg

    how they got the power?
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  2. #2
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    Tehran
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    In Summation We can use the Merge Role :

    <br />
Cosx = \sum_{n=0}^{n=\infty} {(-1)}^(n) {\frac {x^{(2n)}}{(2n!)}}<br />

    So We Can Merge Like Below :

    <br />
Cosx = \sum_{n=1}^{n=\infty} {(-1)}^{(n-1)}{\frac {x^{2(n-1)}}{2(n-1)!}}<br />
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  3. #3
    MHF Contributor
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    in the original expression had (-1)^(2n+1)
    which represent the odd number members

    while you write as the original
    (-1)^(n)


    its not the same
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  4. #4
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    We Can Play By Sigma Indexes .

    I think the (-1)^n is easier to understand
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