Calculus Series problem (show work)?

Question

Approximate the sum of the series correct to four decimal places.
E,n=1, ((-1/8)^n)*n

Answer 1

This is an alternate series and the error in abs val is less than the first term left out.
so 1/8^n *n <1/10^5 taking into account cutting errors Ex.1/3=0.3333
so trying with n=7 8^7/7>10^5
So we have to sum till n=6
-1/8+2/64-3/512 +4/4096-5/32768+6/262144=-0.0988