For the geometric series 1-2/3+4/9-8/27..., find S8.

Question

I know that a=1 and r=-2/3. I also know that the 8th term is -128/2187 by multiplying -2/3 by itself 8 times. I don’t know how to find the sum and show my work using sn=a*1-r^n/1-r. Someone please help!

Answer 1

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