# Who's gonna be the topper from our community! RA vs SA

**Calculus**Level 4

Two infinite products \(A\) and \(B\) are defined as follows:

\[ \large A = \displaystyle\prod\limits_{n=2}^{\infty} \left(1-\frac{1}{n^3}\right), \quad B =\displaystyle\prod\limits_{n=1}^{\infty}\left(1+\frac{1}{n(n+1)}\right). \]

If \(\frac{A}{B} = \frac{m}{k},\) where \(m\) and \(k\) are relatively prime positive integers, determine \(100m+k\).