- Compute the limit
- Compute the limit
for . Determine the values for which the sequences diverges and for which it converges and compute the values of the limits in the convergent case.

- We multiply and divide the terms by to get,
- Observe that
since

But then, if , the function inside the integral is a decreasing function; hence,

Since this limit goes to 0 for (since ) we have that the sequence converges to 0 for these values of .

If then the integrand is increasing, and so,In this case the limit of as diverges to (since ). Hence, the sequence does not converge.

Finally, if thenPutting this all together we have