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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