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I am perplexed as to how to solve this problem:

$$\sum_{k=0}^{10} \left(\frac{-1}{4}\right)^k$$

The answer is $838861/1048576$ but I do not know how to get there.

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migrated from Sep 15 '13 at 3:08

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You can use the Sum command, like this: Sum[(-1/4)^k, {k, 0, 10}] !Mathematica graphics – Nasser Sep 15 '13 at 2:20
up vote 2 down vote accepted

The sum of a general geometric sequence $x,xr,xr^2,xr^3\cdots$ upto $n$ terms is $x(1+r+r^2+\cdots+r^{n-1})=x\frac{r^n-1}{r-1}$ (You can prove this by induction). Here $x=1$ and $r=-\frac{1}{4}$.

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Thank you, I knew the sequence but was not using correct algebra. I made a simple mistake. – Jinzu Sep 15 '13 at 15:04

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