If `n in N >1` , then the sum of real part of roots of `z^n=(z+1)^n` is equal to

If X={4^n -3n-1 , n in N} and Y={9(n-1), n in N} , where N is the set of natural numbers, then X uu Y is equal to :

If z is a complex number such that |z|=1, z ne 1 , then the real part of |(z-1)/(z+1)| is

Find the sum of n terms of the series whose nth terms is (i) n(n-1)(n+1) .

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot

If the seventh terms from the beginning and the end in the expansion of (root(3)(2)+(1)/(root(3)(2)))^(n) are equal, then n equals:

Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers. Then sum_(r=1)^(n)(S_(r))/( S_(r )) equals :

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .

If S denotes the sum to infinity and S_(n) , the sum of n terms of the series 1+( 1)/(2) +( 1)/( 4) + ( 1)/( 8 ) +"………….", such that S-S_(n) lt ( 1)/( 1000) , then the least value of n is :

If X=[[1,1],[1,1]] , then X^n , for n in N is equal to