Question

For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8

Answer 1

Hello,

We have s0 = 1 and q = -2/3

`S _(n) = S _(0) * q {}^(n) = 1 * ( - (2)/(3) ) {}^(n)`

`S _(8) = ( - (2)/(3) ) {}^(8) = \frac{2 {}^(8) }{3 {}^(8) } = (256)/(6 561)`

Answer 2

Explanation:

The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5