Due to the fact that the reason is the sum of the n first terms is sometimes greater sometimes lower than the sum to infinity (one term out of two is positive and the other one negative). You have to consider the absolute value of the difference.
The first three terms of a geometric series are 2 , -1/2 and 1/8 respectively . Find the smallest value of n such that the difference between the sum of the first n terms and the sum to infinity is less than .
Just wondering which is greater , Sum to infinity or the sum of the n terms ...