The series is and .

By the Alternating Series estimation theorem:

(i) .

(ii) , then .

Find smallest value of such that .

Here .

Check by trial and error method:

For , .

For , .

Term number should not be decimal , so for  .

is the least value that satisfy the inequality.

Series starts from and there are terms before .

We can conclude that sum of first terms of series.

Therefore, add the first four terms of the series to approximate the sum with in given error.

Add the first four terms of the series to approximate the sum with in given error.