Confusing series question

**arze** · August 17th 2010, 09:34 PM

If $-1<r<1$ and $S_n=\displaystyle \sum^n_{p=1} r^p$ find
a) $\displaystyle \lim_{n\rightarrow\infty} S_n$
b) $\displaystyle \sum^{\infty}_{n=1}nr^n$
c) $\displaystyle \sum^n_{q=1} S_q$

I have done the first two correctly, but I have no idea what the third one means. This is the entire question.
Thanks for any help.

**Vlasev** · August 17th 2010, 09:48 PM

$\displaystyle \sum^n_{q=1} S_q = \displaystyle \sum^n_{q=1} \sum^q_{p=1} r^p$

I'm sure you can do the sum now!

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