I have two problems that I can't seem to get.

Problem 1.Use the ratio test to determine whether the series converges or diverges. Explain how the test permits you to draw your conclusion.

My Solution

The problem here is, I know the ratio test isn't supposed to fail for this problem, lol. Where am I going wrong?

Use the limit comparison test to determine whether the series converges or diverges. Explain how the test permits you to draw your conclusion.

Problem 2.

My Solution

, Compare to , conjecture to diverge.

Since and , and diverges, diverges.

I was told that my algebra in this problem was incorrect, but I don't know why. Can someone show me where I went wrong, please?

Thanks in advance for any help.