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sum(r=0)^(20).^(50-r)C6...

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

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if sum_(r=0)^(25).^(50)C_(r)(.^(50-r)C_(25-r))=k(.^(50)C_25) , then k equals:

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

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

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

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

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

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

The sum of the series sum_(r=0)^(10) .^(20)C_(r) , is 2^(19)+{(.^(20)C_(10))/2} .