Infinite limit of inverse tangent series

[flyerpower]

Homework Statement

Take the infinite limit of that sequence.

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Homework Equations

The Attempt at a Solution

I have no idea where to start from, hints and ideas would be greatly appreciated.

Thanks.

 

[tiny-tim]

hi flyerpower!

hint: (tanA - tanB)/(1 + tanAtanB)

 

[flyerpower]

hi flyerpower!

hint: (tanA - tanB)/(1 + tanAtanB)

Ok, so tan(A-B)=(tanA-tanB)/(1+tanAtanB)

and A-B=arctan[(tanA-tanB)/(1+tanAtanB)

Now i think i should find some A and B so as :

tanA-tanB=x
and
tanA*tanB=k(k+1)*x^2

buuut i cannot still figure out what A and B should be

 

[SammyS]

How about tan(A) =(k+1)x & tan(B) =kx ?

 

[flyerpower]

LOL, it was so obvious, thank you:)

It gives me pi/2 - arctg(x) which is arctg(1/x)

Thank you both!