An algebra problem by Manish Dash

Algebra Level pending

If the total number of runs scored in "n" matches is \((\frac { n+1 }{ 4 } )({ 2 }^{ n+1 }-n-2)\) where n>1, and the runs scored in the \({ k }^{ th }\) match are given by \(k.{ 2 }^{ n+1-k }\), where \(1\le k\le n\). Find n.

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