Sum of series problem #2

**BabyMilo** · December 5th 2011, 12:09 PM

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.

**wnvl** · December 5th 2011, 01:20 PM

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

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