$\"\"$

$\"\"$ .

Find the first ten terms of the sequence.

$\"\"$ .

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

The series appears to be converging to some finite number.

$\"\"$

Graph the sequence of terms and sequence of sums.

$\"\"$

Observe the table and graph:

It appears that the terms of sequence converges to $\"\"$ .

It appears that the terms of sequence converge to $\"\"$ .

$\"\"$

Find the sum of infinite series.

$\"\"$

This is a geometric series with $\"\"$ and common ratio $\"\"$ .

Here the series is convergent since $\"\"$ .

Sum of infinite geometric series: $\"\"$ .

Substitute corresponding values in the formula.

$\"\"$

$\"\"$ .

Sum of infinite series is $\"\"$ .

$\"\"$

Table:

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

Graph the sequence of terms and sequence of sums.

$\"\"$

The series is convergent. Sum of infinite series is $\"\"$ .