2
$\begingroup$

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

  • 0
    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.2012-10-27
  • 1
    The parentheses are wrong.. it should be $\frac{1 - (-2)^{n+1}}{3}$2012-10-27
  • 0
    Cheers..Thanks for the heads up on brackets..Still trying to get used to the editing on site2012-10-27
  • 2
    Writing "$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

1 Answers 1