I have derived a new formula for π. What should I do with it?

Question

I mean I know that I should publish it somewhere but have no idea about how to write it in a professional manner and where to publish it. Can anyone guide me?

Answer 1

What would be correct is $$\pi = \sqrt{1+\sum\limits_{n=1}^\infty \frac{6\times 2^n-n^2}{2^n \times n^2}}$$ which is close to what you said in your comment

As @lulu notes, this is essentially $\sum\limits_{n=1}^{\infty}\frac {1}{n^2}=\frac {\pi^2}6$ and is not novel - it is called the Basel problem

Your expression converges slowly to $\pi$: using the first ten terms gives about $3.049522$ while the first hundred gives $3.132077$