In Problems 1–4 find the radius of convergence and interval of convergence for the given power series.

Step 1</p>

In this problem, we are asked to find the interval and the radius of convergence for the power series.

Step 2</p>

To find the Radius of convergence, let us use the ratio test.

Therefore

Thus for the series converges.

Therefore the radius of convergence is .

Step 3</p>

Now we have to find the interval of convergence.

For that, we have to check whether the series is convergent at the endpoints and .

Therefore at the series becomes

This the series diverges at , by the p series test.