Pi Approximation with a Pretty Formula

Escriba un c$$digo en Python$-3$ para calcular PI con la expresi$$n:

$=\frac{pro{d}_k}{{\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{4k^2-1}}=1^{}(1+\frac{1}{4k^2-1})$~~$\frac{pro{d}_k}{{\displaystyle \underset{k=1}{\overset{N}{}}}\frac{1}{4k^2-1}}=1^N(1+\frac{1}{4k^2-1})$

Where $N$ is a finite integer number. Use the following output statement in your code: print$($F$"\{$PI$=$:$\mathrm{.}7$f