# 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:

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

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

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