Let `a_(r)=r^(2)(^(50)C_(r))/(^(50)C_(r-1))` and b denotes the coefficient of `x^(49)` in `(x-a_(1))(x-a_(2))......(x-a_(50))`, find `(-(1)/(17))b`.

Coefficient of x^(48) in sum_(r=0)^(50)""^(50)C_(r).(x-2)^(x).3^(50-r) is

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

Let a_(r) denote the coefficient of x^(r) in the expansion of ( 1 + x)^(P + q) , then

If in the expansion of (1-x)^(2n-1)a_(r) denotes the cofficient of x^(r) then prove that a_(r-1)+a_(2n-r)=0

(1+2x+3x^(2))^(15) = sum_(r=0)^(30) a_(r)x^(r) then digit at the unit place of a_(0) + a_(1) + a_(30) is

For r=0,1,.....,10, let A_(r),B_(r),quad and C_(r) denote,respectively,the coefficient of x^(r) in the expansions of (1+x)^(10),(+x)^(20) and (1+x)^(30). Then sum A_(r)(B_(10)B_(r)-C_(10)A_(r)) is equal to

If (1+x)^(2n)=sum_(r=0)^(2n)a_(r)x^(r) then the value of a_(0)^(2)-a_(1)^(2)+a_(2)^(2)-a_(3)^(2)+...+(a_(2n))^(2)=

Let y = 1 + (a_(1))/(x - a_(1)) + (a_(2) x)/((x - a_(1))(x - a_(2))) + (a_(3) x^(2))/((x - a_(1))(x - a_(2))(x - a_(3))) + … (a_(n) x^(n - 1))/((x - a_(1))(x - a_(2))(x - a_(3))..(x - a_(n))) Find (dy)/(dx)

Let a_r denote the coefficient of y^(r-1) in the expansion of (1 + 2y)^(10) . If (a_(r+2))/(a_(r)) = 4 , then r is equal to