Question

Find a power series for the function, centered at c, and determine the interval of convergence.

Answer 1

Step 1:

The function is , .

consider the denominator .

Partial decomposition:

Substitute in above expression.

Substitute in above expression.

Substitute and in equation (1).

Step 2:

Power series of .

Interval of convergence is and .

and

and

Both the conditions can be satisfied in the interval .

Therefore, interval of convergence of the series   is .

Solution:

Power series representation of the function is .

Interval of convergence is .