In the expansion of `(1-x)^(30)(1+x+x^(2))^(31)` the coefficient of `x^(47)` is `(-30C_(r))` then the value of `|(r)/(2)|` is

In the expansion of (1+x)^30 the sum of the coefficients of odd powers of x is

If in the expansion of (1+x)^(15), the coefficients of (2r+3)^(th) a n d\ (r-1)^(th) terms are equal, then the value of r is a. 5 b. 6 c. 4 d. 3

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)

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)

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

In the binomial expansion of (1+x)^(43) , the coefficients of the (2r+1) th and (r+2) th terms are equal. Then r=

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

STATEMENT - 1 : The term independent of x in the expansion of (x+1/x+2)^(m) is ((2m) !)/((m !)^(2)) STATEMENT - 2 : The coefficient of x^(b) in the expansion of (1+x)^(n) is .^(n)C_(b) .

the coefficient of x^(r) in the expansion of (1 - 4x )^(-1//2) , is