Infinite arctangent sums involving Fibonacci and Lucas numbers

TL;DR

This paper derives new infinite arctangent sum formulas involving Fibonacci and Lucas numbers using elementary methods, generalizing some well-known results.

Contribution

It introduces a straightforward elementary approach to derive numerous new infinite arctangent sums with Fibonacci and Lucas numbers, extending existing formulas.

Findings

Many new arctangent sum formulas involving Fibonacci and Lucas numbers.

Some classical results are recovered as special cases.

The approach simplifies derivation of such infinite sums.

Abstract

Using a straightforward elementary approach, we derive numerous infinite arctangent summation formulas involving Fibonacci and Lucas numbers. While most of the results obtained are new, a couple of celebrated results appear as particular cases of the more general formulas derived here.