$\"\"$

The series is $\"\"$ and $\"\"$ .

Alternating Series estimation theorem:

(i) $\"\"$ .

(ii) $\"\"$ , then $\"\"$ .

Find smallest value of $\"\"$ such that $\"\"$ .

Here $\"\"$ .

$\"\"$

$\"\"$ .

Term number should not be decimal , so $\"\"$ for $\"\"$ .

$\"\"$ is lthe least value that satify the inequality.

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

$\"\"$

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