In the expansion of `(1+x)^n`, the sum of the coefficients of the terms in even positions is `2^(n-1)`

If n is a positive integer, show that, in the expansion of (1+x)^(n) the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to 2^(n-1) .

Consider the expansion of (1 + x)^(2n+1) The sum of the coefficients of all the terms in the expansion is

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

The sum of the coefficients of middle terms in the expansion of (1+x)^(2n-1)

The sum of the coefficients of middle terms in the expansion of (1+x)^(2n-1)

The sum of the coefficients of the terms of the expansion of (3x-2y)^n is

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

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

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