Posted by Jenny on .
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((2n1)pi/2)]/n
A. The series diverges
B. The series converges conditionally.
C. The series converges absolutely.
D. It cannot be determined.

Calculus 
Steve,
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)