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

Find the coefficient of x^8 in the expansion of (x^2-1/x)^(10)

Find the coefficient of x^n in the expansion of: (a+bx+cx^2)/e^x .

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

Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

Find the coefficient of x^n in the expansion of e^(a+bx) in powers of x.

Find the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx))^(11) . (ii) the coefficient of x^(-7) in the expansion of (ax - (1)/(bx^2))^(11) . Also , find the relation between a and b , so that these coefficients are equal .

Show that coefficient of a^m and a^n in the expansion of (1+a)^(m+n) are equal.

If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-3 is: