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 , .

For , .

For , .

For , . \ \

is lthe least value that satify the inequality.

Series starts from and there are terms before .

We can conclude that sum of first terms of series.

Therefore, add the first six terms of the series to approxiamte the sum with in given error.

Add the first six terms of the series to approxiamte the sum with in given error.