If n is a positive integer and `(1+i)^(2n)=k cos(n pi/2)`, then the value of k is

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

If n is a positive integer and C_(k)=.^(n)C_(k) then find the value of sum_(k=1)^(n)k^(3)*((C_(k))/(C_(k-1)))^(2)

If n is a positive integer SC_(k)=^(n)C_(k), find the value of (sum_(k=1)^(n)(k^(3))/(n(n+1)^(2)*(n+2))((C_(k))/(C_(k)-1))^(2))^(-1)

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

If n is a positive integer and omegane1 is a cube of unity, the number of possible values of |e^(sum_(k=0)^(n) ((n)/(k))omega^(k))|

sum_(k=1)^(360)(1)/(k sqrt(k+1)+(k+1)sqrt(k)) is the ratio of two relatively prime positive integers m and n then the value of m+n is equal to

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

A function f:ZrarrZ is defined as f(n)={{:(n+1,n in " odd integer"),((n)/(2),n in "even integer"):} . If k in odd integer and f(f(f(k)))=33 , then the sum of the digits of k is