Fun With Binomial Coefficients

Let

P = \(\sum_{i<j} { \left( \frac { 1 }{ \overset { n }{ \underset { i }{ C } } } +\frac { 1 }{ \overset { n }{ \underset { j }{ C } } } \right) } \) and

Q = \(\sum_{i<j} { \left( \frac { i }{ \overset { n }{ \underset { i }{ C } } } +\frac { j }{ \overset { n }{ \underset { j }{ C } } } \right) } \)

,then

\(Q =\frac { n }{ \beta } P\)

Find \({ \beta }^{ \beta }\).

Given That \(\overset { n }{ \underset { r }{ C } } \) are Binomial Coefficients...

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