Determine whether each series converges or diverges. State which convergence test is used and show all corresponding computation:

For the Integral Test, specify the value of the improper integral and show all computations.

If either comparison test is used, state which series you are comparing with and why it converges or diverges.

a) For Direct Comparison, show the comparison.

b) For Limit Comparison, provide the limit and its value.

If the Test for Divergence is used, specify the value of the limit.

1.n=11+n4n3 (Extra Practice: Try both the integral test and a comparison test.)

2.n=14n3(n3+1)(3n21)(n2+5)

3.n=15n39n

4.k=06k5k+12 (Extra Practice: Try finding the sum.)

5.n=1ln(4n3+1n3+1)

6.k=1(4+2k)3/21 (Extra Practice: Try both the integral test and a comparison test.)

7.n=15nn42n+1