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Math Help - Sum of series problem #2

  1. #1
    Senior Member
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    Sum of series problem #2

    Can someone walk me through this?

    the answer should be \frac{a(1-r^n)}{1-r}+\frac{dr}{(1-r)^2}[1+nr^{n-1}-(n-1)r^n]

    Many thanks.
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  2. #2
    Junior Member
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    Re: Sum of series problem #2

    =a \sum_{k=0}^{n-1}r^{k}+r\cdot d\cdot \frac{\mathrm{d} }{\mathrm{d} r}\sum_{k=0}^{n-1}r^{k}
    =a\frac{r^n-1}{r-1}+dr\frac{\mathrm{d} }{\mathrm{d} r}\sum_{k=0}^{n-1}\frac{r^n-1}{r-1}
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