$\"\"$

The series is $\"\"$ .

(a)

Consider the fraction $\"\"$ .

Solve the fraction using partial fractions.

$\"\"$ .

$\"\"$

Equate the constant terms.

$\"\"$

$\"\"$ .

Equate the coefficients of $\"\"$ .

$\"\"$

Substitute $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

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

$\"\"$

$\"\"$ .

Find $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

(b)

Graph the partial sum function is $\"\"$ .

$\"\"$

Observe the graph:

Tabulate the $\"\"$ values for different values of $\"\"$ .

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

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

$\"\"$

(c)

Find the first ten terms of the sequence.

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

If $\"\"$ then $\"\"$ .

Graph :

Graph the values $\"\"$ .

$\"\"$

(d)

The terms of the series decrease in magnitude slowly.

So, the sequence of partial sums approaches the sum slowly.

$\"\"$

(a) $\"\"$ .

(b)

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

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

(c)

Graph :

Graph the values $\"\"$ .

$\"\"$

(d) The terms of the series decrease in magnitude slowly.So, the sequence of partial sums approaches the sum slowly.