Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 2: Exercise

Maximum sum of the coefficients in the expansion of ${\left(1-x\sin \theta +x^2\right)}^n$ is

The value of $\sum _{r=1}^{15}\frac{r·2^r}{(r+2)!}$

The value of $\sum _{r=0}^{50}{\left(-1\right)}^r\frac{{}^{50}\mathrm{C}_r}{r+2}$ is equal to

If $-\frac{1}{3}<x<1.$ Then $1+n\left(\frac{2x}{1+x}\right)+\frac{n(n+1)}{2!}{\left(\frac{2x}{1+x}\right)}^2+\dots \dots \dots \dots$ is equal to

The sum of rational term in ${\left(\sqrt{2}+\sqrt[3]{3}+\sqrt[6]{5}\right)}^{10}$ is equal to

If $p=(8+3\sqrt{7}{)}^n$ and $f=p-\left[p\right],$ where $[·]$ denotes the greatest integer function, then the value of $p(1-f)$ is equal to

The value $\sum _{r=0}^{20}r\left(20-r\right){\left({}^{20}C_r\right)}^2$ is equal to

If $n$ be a positive integer such that $n\ge 3,$ then the value of the sum upto $n$ terms of
$1·n-\frac{(n-1)}{1!}\left(n-1\right)+\frac{(n-1)(n-2)}{2!}\left(n-2\right)-\frac{(n-1)(n-2)(n-3)}{3!}\left(n-3\right)+\dots \dots$ is