If `z_r : r=1,2,3, ,50` are the roots of the equation `sum_(r=0)^(50)z^r=0` , then find the value of `sum_(r=0)^(50)1/(z_r-1)`

Let z_(r),r=1,2,3,...,50 be the roots of the equation sum_(r=0)^(50)(z)^(r)=0 . If sum_(r=1)^(50)1/(z_(r)-1)=-5lambda , then lambda equals to

If x^(2)+x+1=0 then find the value of sum_(r=1)^(27)(x^(r)+(1)/(x^(r)))^(2)

sum_(r=0)^(20).^(50-r)C_6

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

The value of sum_(r=0)^(3m)(-1)^(r).6mC_(2r) is

Number of real roots of equation sum_(r=1)^(10)(x-r)^(2)=0 is

If z_(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0 , then sum_(r=0)^(6)"Re"(z_(r))=

If sum_(r=1)^(50)tan^(-1)1/(2r^2)=p , then the value of tan p is:

If alpha and beta are the roots of the equation 375x^(2)-25x-2=0, then the value of lim_(n rarr oo)(sum_(r=1)^(n)alpha^(r)+sum_(r=1)^(n)beta^(r)) is