$\"\"$

\

The function is $\"\"$ .

\

Find the transformation that relates $\"\"$ to $\"\"$ , use $\"\"$ -substitution.

\

Substitute $\"\"$ for $\"\"$ in $\"\"$ , equate the two functions solve for $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, $\"\"$ .

\

Replace $\"\"$ with $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

The power series is $\"\"$ .

\

The series is converges for $\"\"$ .

\

$\"\"$

\

There are no solutions for the condition $\"\"$ , hence it is not considered.

\

$\"\"$

\

$\"\"$ .

\

The series converges for $\"\"$ .

\

$\"\"$

\

Find the sixth partial sum of the series $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Graph :

\

Graph the function $\"\"$ and sixth partial sum $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ for $\"\"$ .

\

Graph of the function $\"\"$ and sixth partial sum $\"\"$ .

\

$\"\"$ .