If n is a positive integer, find the coefficient of `1/x` in the expansion of `(1+x)^n(1+1/x)^n`

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

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

If n is a positive integer, then find int x^n dx

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

Let m be the smallest positive integer such that the coefficient of x^(2) in the expansion of (1+x)^(2)+(1+x)^(3) + "……." + (1+x)^(49) + (1+mx)^(50) is (3n+1) .^(51)C_(3) for some positive integer n, then the value of n is "_____" .

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

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)