Let's look at the first few terms
-4 + 2 - 1 + 1/2.......
The common ratio, r, = -1/2 .....since l r l < 1....this will converge
And the first term is -4
So...the sum is given by
[ first term ] / [ 1 - r ] =
-4 / [ 1 - (-1/2) ] =
-4 / [ 3/2] =
-8 / 3
