sum_(r=1)^(100)(r*100C_(r))/(100C_(r-1))=

If C_(r) stands for ""^(n)C_(r) and sum_(r=1)^(n)(r*C_(r))/(C_(r-1))=210 , then n equals:

The coefficient of x^(53) is sum_(r=0)^(100) 100 C_(r).(x-3)^(100-r). 2^(r) is

Let Q = sum_(r=0)^(50)(""^(50)C_(r))^(2), R = sum_(r=0)^(100)(-1)^(r) (""^(100)C_(r))^(2) Then find the value of Q + R

Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)

Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

Let P =sum_(r=1)^(50)(""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), R = sum_(r=0)^(100)(-1)^(r) (""^(100)C_(r))^(2) The value of P - R is equal to

The value of sum_(r=0)^(50)(.^(100)C_(r).^(200)C_(150+r)) is equal to