| Author |
Comment/Response |
Daniel Krawisz
|
 11/23/08 11:18pm
Hi, I'm using Mathematica 6.0.0 for students.
When I do
Sum[Sin[n Pi /2]^2 / n, {n, Infinity}]
I get
(EulerGamma + Log[2])/2
and when I apply N to that I get 0.635181 .
Meanwhile, if I do
Sum[Sin[n Pi /2]^2 / n, {n, Infinity}]
I get 3.66547 .
However, it is clear that the correct answer ought to be infinity. When n is even,
Sin[n Pi /2]
is zero. When n is odd, Sin[n Pi / 2] is 1. Hence the sum just amounts to
Sum[1/n,{n,1,Infinity,2}]
Which does not converge. What's going on here?
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