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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.

  • Calculus -

    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)

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