If total number of runs scored in \( n \) matches is \( \left(\frac...

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If total number of runs scored in \( n \) matches is \( \left(\frac{n+1}{4}\right)\left(2^{n+1}-n-2\right) \) where \( n1 \) and the runs scored in the \( k^{\text {th }} \) match are given by \( k .2^{n+1-k} \), where \( 1 \leq k \leq n \), find \( n \)
\( \mathrm{P} \)
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