$\"\"$ \ \

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

Tabulate the sequence of terms and partial terms.

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table $\"\"$ is decreasing and tends to zero.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$ \ \

Observe the graph: \ \

The blue dots are partial sums of the series. \ \

Sum of the series correct to four decimal places is $\"\"$ . \ \

$\"\"$ \ \

By the Alternating Series estimation theorem: \ \

Here (i) $\"\"$ , and (ii) $\"\"$ , then $\"\"$ . \ \

Find the sum correct to four decimal places. \ \

Thus, $\"\"$ .

Fromthe table $\"\"$ .

Calculate the sum upto six partial terms.

$\"\"$

$\"\"$ . \ \

$\"\"$ \ \

$\"\"$ .