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05/27/10 6:45pm

When I give Mathematica the following equation:

Sum[(-1)^(n - 1) Log[n]^(1/2)/n, {n, 1, \[Infinity]}]

it returns the standard form of this equation, telling me that it found no errors, so then I use NSum to find that it's around -0.225719.

If I give it the equation:

Sum[(-1)^(n - 1) Log[n]^(0.5)/n, {n, 1, \[Infinity]}]

(exactly the same with 0.5 exchanged with 1/2) it tells me that the series doesn't converge. It still returns the same answer with NSum, but I wondered why it tells me the series doesn't converge one way but does the other way.


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