$\"\"$

\

The function is $\"\"$ and centered at $\"\"$ .

\

$\"\"$ . \ \

\

Find the geometric power series of the function.

\

$\"\"$

\

$\"\"$

\

The series is in the form of geometric series.

\

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

\

Substitute $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, the power series is $\"\"$ and is converges in the interval $\"\"$ . $\"\"$

\

The power series is $\"\"$ and is converges in the interval $\"\"$ .