calculus question help

Question

Use the alternating series test to determine the convergence/divergence of the series  .

A	The alternating series fails.
B	The series converges.
C	The series is conditionally convergent.
D	The summation must start with n = 0 so the alternating series test cannot be applied.

Answer 1

The series converges conditionally. This means that, while the sum of the absolute value of the terms goes to infinity, there is a limit of the partial sums due to the terms alternating in sign, and the terms converging to 0, with each term being lower in absolute value than the previous term.

That the sum of absolute values goes to infinity is seen by noting that the absolute value of terms goes to 1/n, whose sum diverges.