$\"\"$

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

(a)

Find the sum of the series when $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

The series is in the form of geometric series.

The general form of geometric series is $\"\"$ .

The sum of the geometric series is $\"\"$ .

Compare the series with general form.

Here $\"\"$ and $\"\"$ .

The sum of the series is $\"\"$ .

$\"\"$

Graph :

Graph the first six terms of the series and the sum of the series $\"\"$ .

$\"\"$

(b)

Find the sum of the series when $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

The series is in the form of geometric series.

The general form of geometric series is $\"\"$ .

The sum of the geometric series is $\"\"$ .

Compare the series with general form.

Here $\"\"$ and $\"\"$ .

The sum of the series is $\"\"$ .

$\"\"$

Graph :

Graph the first six terms of the series for $\"\"$ .

$\"\"$

(c)

The series is converges for $\"\"$ because it is an alternating series.

Observe the graph that for $\"\"$ partial sums approach sum of series from below the sum of the series but for $\"\"$ partial sums alternate around solution.

$\"\"$

(d)

The partial sum is $\"\"$ .

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

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

$\"\"$

(a) Graph :

Graph the first six terms of the series for $\"\"$ .

$\"\"$

(b) Graph :

Graph the first six terms of the series for $\"\"$ .

$\"\"$

(c) The series is converges for $\"\"$ because it is an alternating series.

Observe the graph that for $\"\"$ partial sums approach sum of series from below the sum of the series but for $\"\"$ partial sums alternate around solution.

(d)

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

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$