Question

How do you find the sum of `(-2)^(i-1)` from i=1 to 12?

Answer 1

The sum will equal -1365. How you get this is shown below...

Explanation:

This is a geometric series with a common ratio of -2 and a first term equal to 1 since `(-2)^(1-1) = (-2)^0 = 1`

So, the sum of `n` terms is given by

`S_n = (a_1(1-r^n))/(1-r)`

Here, `n` = 12 if we want the sum of the first 12 terms, so

`S_12 = (1(1-(-2)^12))/(1-(-2))`

`=(1-4096)/3 = -4095/3 = -1365`