# Evaluating a geometric progression [duplicate]

I would like to evaluate the sum of the following geometric progression

$1 -2 + 2^{2} - 2^{3} + ...+(-1)^{n}2^{n}$

Would the following proposed solution be on the right lines?

$a = 1$ (Being the first term)

$r = -2$ (Being the common ratio)

$n = n + 1$ (The number of terms we want to consider in this case)

The formula to evaluate the sum of a geometric progression being:

$$\frac{1 - r^n}{1 - r}.$$

Therefore, plugging in the values above

$$\frac{1 - (-2)^{n+1}}{3}.$$

Thanks

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## marked as duplicate by apnorton, Kirill, Rafflesia arnoldii, Hanul Jeon, John ZHANGNov 8 '14 at 2:14

This question was marked as an exact duplicate of an existing question.

Your proposed solution is unreadable. What do you mean by $a$ and $r$? It looks like you're referring to some particular result but are leaving it to the reader to guess which it is and how your letters connect to it. – Henning Makholm Oct 27 '12 at 15:08
The parentheses are wrong.. it should be $\frac{1 - (-2)^{n+1}}{3}$ – Cocopuffs Oct 27 '12 at 15:11
Cheers..Thanks for the heads up on brackets..Still trying to get used to the editing on site – bosra Oct 27 '12 at 15:14
Writing "$n = n + 1$" is always dubious, regardless of the further content. In this case you are referring to two different variables it seems, so just write something like $m = n + 1$ then. – TMM Oct 27 '12 at 17:53