" Dustrue "y" Proor that: "((2r)!)/(n!)={1*3*5-(2n-1)}2^(8)

Prove that ((2n+1)!)/(n!)=2^(n){1.3.5(2n-1)(2n+1)}

Prove that ((2n+1)!)/(n!)=2^(n)[1.3.5.....(2n-1)*(2n+1)]

Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

Given that C_(1)+2C_(2)x+3C_(3)x^(2)+...+2nC_(2n)x^(2n-1)=2n(1+x)^(2n-1),whereC_(r)=(2n)!/[r!(2n-r)!];r=0,1,2 then prove that C_(1)^(2)-2C_(2)^(2)+3C_(3)^(2)-...-2nC_(2n)^(2)=(-1)^(n)nC_(n).

Using mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......+1/((3n-1)(3n+2))=n/(6n+4) for all n in N .

If the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

If the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

Show that the HM of (2n+1)C_(-) and (2n+1)C_(-)(r+1) is (2n+1)/(n+1) xx of (2n)C_(r) Also show that sum_(r=1)^(2n-1)(-1)^(r-1)*(r)/(2nC_(r))=(n)/(n+1)

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))