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

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

The value of lim_(n to oo) [(n!)/(n^(n))]^((1)/(n)) is equal to -

If n >1 , show that the roots of the equation z^n=(z+1)^n are collinear.

If the product of n positive numbers is n^n , then their sum is (a) a positive integer (b). divisible by n (c)equal to n+1//n (d)never less than n^2

The frequency of the fundamental tone in a 60 cm long string is n . At what position should a bridge be placed below the wire so that the frequency of one part will be n_(1) and that of the other part will be n_(2) in such a way that the ratio n : n_(1) is equal to the ratio n_(1) : n_(2) ?

In a geometric series, the first term is a and common ratio is rdot If S_n denotes the sum of the terms and U_n=sum_(n=1)^n S_n ,then r S_n+(1-r)U_n equals a. 0 b. n c. n a d. n a r

If z=x+iy (x, y in R, x !=-1/2) , the number of values of z satisfying |z|^n=z^2|z|^(n-2)+z |z|^(n-2)+1. (n in N, n>1) is

Show that the sum of sum_(n=1)^infty n/(n^4+4) equals to 3/8

Let z=9+b i ,and b is nonzero real and i^2=-1. If the imaginary part of z^2a n dz^3 are equal, then b/3 is ______.

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7