\[ \large \displaystyle\sum _{ n=1 }^{ k }{ { (-1) }^{ n+1 } } \dbinom{ k }{ n }\displaystyle\sum _{ 1\le i\le j\le n }{ \dfrac { 1 }{ ij } } =\dfrac { 1 }{ { k }^{ 2 } } \]

Prove the equation above.

This is a part of the set Formidable Series and Integrals

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