Estimated Sums in Infinite Series Problem

[pjcircle]

Homework Statement

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Ʃ((-1)ⁿ)/(n(10ⁿ)) from n=1 to infinity
|error| <.0001

I keep ending up with n=log(4)-log(n)

 

[haruspex]

Please post your working.