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

If sum n=210 , then sum n^2 is equal to:

lim_(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to

If n gt 1 and if z ^(n) = (z +1) ^(n) then :

If n is an odd natural number, then sum_(r=0)^n (-1)^r/(nC_r) is equal to

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

If 4nalpha =pi then cot alpha cot 2 alpha cot 3alpha ...cot (2n-1)alpha n in Z is equal to

Let C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) is equal to

If z and bar z represent adjacent vertices of a regular polygon of n sides where centre is origin and if (Im(z))/(Re(z)) = sqrt(2) - 1 , then n is equal to:

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- bar w z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 (c) z=bar z (d) None of these

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