Question

Use the power series

to determine a power series, centered at 0, for the function. Identify the interval of convergence.

Answer 1

Step 1:

The function is .

Power series of .

Substitute above result into the function.

The above series is convergent when ,

But at the end points , the series is .

As .

Thus, the series is divergent at the end points by the divergence test.

Therefore, interval of convergence is .

Solution:

Interval of convergence is .