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Math Help - single power series...

  1. #1
    Senior Member
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    single power series...

    i was wondering if someone could check my work...

    i am supposed to rewrite the following series as a single power series...

    4\sum_{n=2}^{\infty }n(n-1)c_{n}x^{n-2}-3\sum_{n=1}^{\infty}nc_{n}x^{n-1}+\sum_{n=0}^{\infty}c_{n}x^{n}

    here is what i got as an answer...did i do it right?

    8c_{2}-3c_{1}+c_{0}+4\sum_{k=1}^{\infty}(k+2)(k+1)c_{k+2}  x^{k}-3\sum_{k=1}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=1}^{  \infty}c_{k}x^{k}
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  2. #2
    MHF Contributor
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    Looks good to me but you could have done

    4\sum_{k=0}^{\infty}(k+2)(k+1)c_{k+2}x^{k}-3\sum_{k=0}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=0}^{  \infty}c_{k}x^{k}.
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