Show that the middle term in the expansion of `(1+x)^(2n)` is 1.3.5…(2n-1)/n! `2n.x^n`, where n is a positive integer.

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

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

The greatest coefficient in the expansion of (1+x)^(2n) is

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

The sum of the coefficients in the expansion of (6 x-5 y)^(n) where n is a positive integer, is

Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^(2n-1)

The term independent of x in the expansion of (1+x)^(n)(1-(1)/(x))^(n) is:

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