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

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

sum_(r=1)^n r (n-r +1) is equal to :

If f(n)=sum_(r=1)^(n) r^(4) , then the value of sum_(r=1)^(n) r(n-r)^(3) is equal to

If n is a natural number gt 2 , such that z^(n) = (z+1)^(n) , then (a) roots of equation lie on a straight line parallel to the y-axis (b) roots of equaiton lie on a straight line parallel to the x-axis (c) sum of the real parts of the roots is -[(n-1)//2] (d) none of these

Let t_n =n.(n!) Then sum_(n=1)^(15) t_n is equal to

sum_(i=1)^(n) sum_(i=1)^(n) i is equal to

sum_(n=1)^7(n(n+1)(2n+1))/4 is equal to

If a ,\ m ,\ n are positive integers, then {root(m)root (n)a}^(m n) is equal to (a) a^(m n) (b) a (c) a^(m/n) (d) 1

If z_1 is a complex number other than -1 such that |z_1|=1\ a n d\ z_2=(z_1-1)/(z_1+1) , then show that the real parts of z_2 is zero.

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