1total runs made =1.2n+2.2n+.....+n.2=4(2n-1)-2n
4(2n-1)-2n=(n+1)(2n+1-n-2)/4
16(2n-1)-8n=(n+1)2n+1-(n+2)(n+1)
(n+2)(n-7)=(n-7)(2n+1
n=7
2n+1=n+2 has no valid solutions
hence n=7
If thotal number of runds scored in n matches is \left(\frac{n+1}{4} \right)\left(2^{n+1} -n-2\right) where n >1, and the runs scored in the kth match are given by k.2n+1-k, 1≤k≤n.
Find n
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3 Answers
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21Tot. runs = 2n+1Σ(k/2k )
tot runs = 2^n+1 ....... the fol. is an A.G.P series.....
RHS = 2n+1(2 -21-n) + n.2n)
Now compare wid tot. runs scored as given on LHS