In the expansion of $(1 + x)^5$,the sum of the coefficients of the terms is

Let $r$ be the remainder when $2021^{2020}$ is divided by $2020^2$. Then $r$ lies between

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

Expand using Binomial Theorem $\left(1+\frac{x}{2}-\frac{2}{x}\right)^{4}, x \neq 0$.

The expression $\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x + 1} }}{2}} \right]}^7}} \right]$ is a polynomial in $x$ of degree

The sum of the coefficients of all odd degree terms in the expansion of $(x + \sqrt{x^3 - 1})^5 + (x - \sqrt{x^3 - 1})^5$,where $x > 1$,is: