pi's and products

Algebra Level 4

\( let:\\ A=\prod _{ n=2 }^{ \infty }{ \left( 1-\frac { 1 }{ { n }^{ 3 } } \right) } \quad \quad \quad \& \quad \quad \quad B=\prod _{ n=1 }^{ \infty }{ \left( 1+\frac { 1 }{ n(n+1) } \right) } \\ If\quad \frac { A }{ B } =\frac { m }{ n } \quad where\quad m,n\quad are\quad relatively\quad prime\\ positive\quad integers,\quad determine\quad 100m+n.\\ \\\underline{\hspace{ 5 in}} \\It\quad is\quad a\quad NIMO\quad Problem \)

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