Convergence Test (NOT test questions)

Question

Which statement is true about the series  ?

	It converges to 0.
	It converges to 1.
	It converges to some unknown value.
I chose this	It diverges.

I chose D because when I use the nth term test it gives me ln(1/∞)= ln(0) which doesn't exist therefore it diverges...? I am not sure if my answer is correct.

Which one of the following series is convergent?

I chose this

I know the answer is C because of the p-series test but I wonder how to test choice B?

Which of the following series is not absolutely convergent?

I chose this

I chose B but I am not sure if A could be the answer. Please help me and thank you in advance!

Answer 1

Your answers are correct.

Your reason for part 1 is a good reason.

In # 2 the one you worried about diverges by the integral test (integrate by parts)

In # 3, the first choice is a geometric series with r=-1/5...it converges absolutely.