$$arctan frac{1}{3} + arctan frac{1}{2} = arctan 1$$
It's easy to generalize this to
$$ arctan frac{1}{n} + arctan frac{n-1}{n+1} = arctan 1, text{ for } n in mathbb{N}$$
which can further be generalized to
$$ arctan frac{a}{b} + arctan frac{b-a}{b+a} = arctan 1, text{ for } a,b in mathbb{N}, a leq b $$
Edit: A similar result relating Fibonacci numbers to arctangents can be found here and here.
No comments:
Post a Comment