Integration Daniel?dextercioby said:I haven't got a clue so far to prove that
[tex] \sum_{n=1}^{\infty} \arctan\left(\frac{1}{2n^{2}}\right) =\frac{\pi}{4} [/tex]
Daniel.
I tried it out, no light.Where did you get thid problem from?dextercioby said:Integrate what...?I don't see a pattern to form a Riemann sum.
Daniel.
Hello Hurkyl. You got to it before I could make amends. Yea, ArcCot and ArcCos will not converge. However, I suspect the ArcSin will.Hurkyl said:A sum of reciprocals is generally not the reciprocal of the sum.
One of the advantages of the tangent function is that its sum formula involves only tangents, so the corresponding formula for arctangents is nicer.
You could try constructing similar things for the others, I suppose. Start with a telescoping series, then apply an addition formula and see what you get.
"There were two paths in the forest.PhilG said:Of course, I realize that the right way to do the problem is with the trig identity.