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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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    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.2012-10-27

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It would help to recall the derivation of the formula for GP, where you took sum of GP as S, multiplied it with "r" and wrote in shifted places so that all except first and last term of S and r*S would match and then finally subtracted then to get (1-r)*S on LHS. Hence, as long as r is not 1, the formula would hold, also in your case.