If `x^p` occurs in the expansion of `(x^2+1//x)^(2n)` , prove that its coefficient is `((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!)` .

If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^n , prove that (iii) 2(P^2 + Q^2 ) = (x+a)^(2n) + (x-a)^(2n) .

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

Prove that the coefficients of x^n in (1+x)^(2n) is twice the coefficient of x^n in (1+x)^(2n-1)dot

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

The sum of the coefficients in the expansion of (1 - x + x^(2) - x^(3))^(n) ,is

If A and B are coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) respectively, then find the value of (A)/(B) .