The coefficient of $x^n$ in the expansion of $(1 + x + x^2 + ....)^{-n}$ is

The coefficient of $x^{19}$ in the polynomial $(x-1)(x-2^1)(x-2^2) \dots (x-2^{19})$ is:

Expand the expression $\left(x+\frac{1}{x}\right)^{6}$.

$(3+\sqrt{8})^5+(3-\sqrt{8})^5=$

The number of terms in the expansion of $(1 + x)^{101} (1 + x^2 - x)^{100}$ in powers of $x$ is

If the sum of the coefficients in the expansion of $(1 - 3x + 10x^2)^n$ is $a$ and if the sum of the coefficients in the expansion of $(1 + x^2)^n$ is $b$,then: