Excel in math, science, and engineering

\[\sum_{n=1}^{\infty} \dfrac{\ln(n)}{n^2} = \dfrac{\pi^2}{6}\left(12\ln(A) - \gamma - \ln(2\pi) \right)\]

Just for fun, I entered the above sum ...

If \(x,y\) and \(z\) are positive proper fractions satisfying \(x+y+z=2\), prove that \[ \dfrac x{1-x} \cdot \dfrac y{1-y} \cdot \dfrac z{1-z} \ge 8 . \]

Brocard's Problem is one of the unsolved problems in Number Theory. As seen in the link above, it asks for all integer solutions to the equation, ...

Can anyone help me in this question :-

Prove or disprove: If \(H\) is a normal subgroup of \(G\) such that \(H\) and \(G/H\) are abelian, then \(G\) is abelian ...

\[\large\lim_{n \to\infty} \dfrac{\displaystyle\prod_{r=0}^n{(2r+1)}}{\displaystyle\prod_{r=1}^{n+1}{2r}} \]

I am unable to compute this limit mathematically, but my ...

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