Question

Determine the following about the series. Indicate the test that was used and justify your answer.

Sigma (lower index n = 1; upper index infinity) [sin((2n-1)pi/2)]/n

A. The series diverges
B. The series converges conditionally.
C. The series converges absolutely.
D. It cannot be determined.

Answer 1

since sin(nth odd multiple of pi/2) = -(-1)^n the sequence is

1 - 1/2 + 1/3 - 1/4 +...

The alternating harmonic series converges to ln(2)