Question

Find a power series representation for the function and determine the interval of convergence.

Answer 1

Step 1:

The function is .

Divide the numerator and denominator by 3.

The power series is .

.

Step 2:

The above series is a geometric series with common ratio .

Geometric series is convergent  when common ratio .

Therefore, the series is convergent if

Interval of convergence is .

Solution:

Power series representation of the function is and

interval of convergence is .