The total number of runs scored If n matches is `(n+1)/4(2^(n+1)-n-2)`,where `ngt1` and the runs scored in `k^(th)` match are given by `k.2^(n+1-k)`, where `1leqkleqn`. Find n

If total number of runs secored is n matches is (n+1)/(4) (2^(n+1) -n-2) where n ge 1 , and the runs scored in the k^(th) match is given by k.2^(n+1 - k) , where 1 le k le n, n is

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

A cricketer has to score 4500 runs. Let a _(n) denotes the number of runs he scores in the n ^(th) match. If a _(1)=a_(2)= …. a _(10) =150 and a _(10) , a _(11), a_(12)…. are in A.P. with common difference (-2) . If N be the total number of matches played by him to scoere 4500 runs. Find the sum of the digits of N.

A cricketer has to score 4500 runs. Let a _(n) denotes the number of runs he scores in the n ^(th) match. If a _(1)=a_(2)= …. a _(10) =150 and a _(10) , a _(11), a_(12)…. are in A.P. with common difference (-2) . If N be the total number of matches played by him to scoere 4500 runs. Find the sum of the digits of N.

If the middle term in the expreansion of (1+x)^(2n) is ([1.3.5….(2n-1)])/(n!) (k) , where n is a positive integer , then k is .