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

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

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and 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.

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 .

Show that the roots of the equation (1+x)^(2n)+(1-x)^(2n)=0 are given by x=+-i tan{(2k-1)(pi)/(2n)) where k=1,2,3,...n

If n is be a positive integer,then (1+i)^(n)+(1-i)^(n)=2^(k)cos((n pi)/(4)), where k is equal to