5. Which of the following series converge?

 

A. None

B. I only

C. II only

D. III only

E. The correct answer is not

given by A, B, C, or D.

 

Solution: The answer is D

 

The first series does not converge because the mth term goes to negative infinity as m goes to infinity:

The second series is ln(3)/3 times the harmonic series, which is known to diverge.

The third series,

converges by the ratio test.