Find the sum to infinite series

[utkarshakash]

Homework Statement

cot^-1 3 + cot^-1 7 + cot^-1 13+...

Homework Equations

The Attempt at a Solution

I first tried to write the nth term of the series

t_n = cot^{-1}\left( 2^n + (2n-1) \right)

Then I tried to calculate the limit as n→∞. But I simply can't do that. I mean I don't know how to calculate the limit.

 

[Ray Vickson]

Homework Statement

cot^-1 3 + cot^-1 7 + cot^-1 13+...

Homework Equations

The Attempt at a Solution

I first tried to write the nth term of the series

t_n = cot^{-1}\left( 2^n + (2n-1) \right)

Then I tried to calculate the limit as n→∞. But I simply can't do that. I mean I don't know how to calculate the limit.

Your presentation is very confusing; use parentheses, like this:
cot^(-1)(3) + cot^(-1)(7) + ... or use "arccot" instead of "cot^-1".

 

[utkarshakash]

Your presentation is very confusing; use parentheses, like this:
cot^(-1)(3) + cot^(-1)(7) + ... or use "arccot" instead of "cot^-1".

OK Here's it

cot^{-1} 3 + cot^{-1} 7 + cot^{-1} 13+...

 

[haruspex]

t_n = cot^{-1}\left( 2^n + (2n-1) \right)

It's not at all obvious to me how 3, 7, 13.. is supposed to be generalised. Do you know that it is intended to be 2ⁿ+2n-1, or are you guessing?