In the expansion of `(1+x)^(n), T_(r+1)` is:

The middle term in the expansion of (1 + x)^(2n) is :

If C_(0), C_(1), C_(2),…, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)(r+1)(C_(r))

If C_(0) , C_(1), C_(2), …, C_(n) are the binomial coefficients in the expansion of (1 + x)^(n) , prove that (C_(0) + 2C_(1) + C_(2) )(C_(1) + 2C_(2) + C_(3))…(C_(n-1) + 2C_(n) + C_(n+1)) ((n-2)^(n))/((n+1)!) prod _(r=1)^(n) (C_(r-1) + C_(r)) .

The coefficient of x^(n) in the expansion of (1+x)(1-x)^(n) is

If |x| lt 1 , then the co - efficient of x^(n) in the expansion of (1+x+x^(2)+…. )^(2) is :

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, the value of m and n are

If in the expansion of (1-x)^(2n-1) , the coefficient of x^r is denoted by a_r , then show that a_(r-1)+a_(2n-r)=0 .

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

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

If the three consecutive coefficients in the expansion of (1 + x)^n are in the ratio 1: 3 : 5, then the value of n is: