# Find the sum to infinite series

1. Jan 10, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
cot^-1 3 + cot^-1 7 + cot^-1 13+.........

2. Relevant equations

3. 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.

2. Jan 10, 2013

### Ray Vickson

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

3. Jan 10, 2013

### utkarshakash

OK Here's it

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

4. Jan 11, 2013

### haruspex

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?