Pi Square Over 6

The Basel Problem

\Large\frac{\pi^2}{6} = 1 + \Sigma_{\small i=1} \small{\frac{1}{i^2} } = 1 + \frac{1}{1^2}+ \frac{1}{2^2}+ \frac{1}{3^2}+ \frac{1}{4^2}+ \frac{1}{5^2} + \~...

\Large\left( \frac{\pi^2}{6} \right) \normalsize = 1 + \frac{1}{1^2}+ \frac{1}{2^2}+ \frac{1}{3^2}+ \frac{1}{4^2}+ \frac{1}{5^2} + \~...

calc_pi <- function(n){
    summation = 0
    for (i in 1:n) {
        summation = summation + 1/i^2
        #print(sqrt(6*summation))
    }
    return(sqrt(6*summation))
}

pi_approx <- numeric()
pi_approx <- calc_pi(500000)
print(pi_approx)

## [1] 3.141591