If n is a positive integer satisfying the equation `2+(6*2^(2)-4*2)+(6*3^(2)-4*3)+"......."+(6*n^(2)-4*n)=140` then the value of n is

If n is an odd positive integer then the value of (1+ i^(2n) + i^(4n) + i^(6n) ) ?

If m and n are the smallest positive integers satisfying the relation (2*e^(i(pi)/(6)))^(m)=(4*e^(i(pi)/(4)))^(n), then (m+n) has the value equal to

If n is a positive integer show that (n+1)^(2)+(n+2)^(2)+....4n^(2)=(n)/(6)(2n+1)(7n+1)

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))

If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n^(2) = (n)/(6)(2n+1)(7n+1)

If n is a positive integer, then 2.4^(2n + 1) + 3^(3n+1) is divisible by :