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If total number of runs scored in n matches is (n+1)(2^{n+1}-n-2) where n > 1, and the runs scored in the kth match are given by k.2^{n+1–k}, where 1 ≤ k ≤ n. Find n.

If total number of runs scored in n matches is (n+1)(2^{n+1}-n-2) where n > 1, and the runs scored in the kth match are given by k.2^{n+1–k}, where 1 ≤ k ≤ n. Find n.

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,

\\S_n=\sum_{1}^{n}k2^{n-k+1}=2^{n+1}\sum_{1}^{n}k2^{-k} \\=2^{n+1}*2(1-{1 \over 2^{n}}-{n \over 2^{n+1}}) \\=2(2^{n+1}-2-n) \\={n+1 \over 4 }=2 \\=>n=7
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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