Embibe Experts Solutions for Exercise 3: EXERCISE

$3C_0+3^2\frac{C_1}{2}+3^3\frac{C_2}{3}+\dots \dots 3^{n+1}·\frac{C_n}{n+1}$ equals to

$C_0-3C_1+5C_2+\dots \dots +(-1{)}^n[2n+1]C_n$ equals to

If $S_n=C_0{C}_1+C_1{C}_2+\dots \dots +C_{n-1}{C}_n$ and $\frac{S_{n+1}}{S_n}=\frac{15}{4}$, then value of $n$ is equal to

If number of terms in the expansion of $(x-2y+3z{)}^n$ are $45$ then $n$ is equal to

Coefficient of $x^{11}$ in the expansion of ${\left(2x^2+x-3\right)}^6$ is

If $a_r$ is the coefficient of $x^r,$ in the expansion of ${\left(1+x+x^2\right)}^n,$ then $a_1-2a_2+3a_3-\dots -2n{a}_{2n}=$

The coefficient of $x^{50}$ in ${\left(1+x\right)}^{41}{\left(1-x+x^2\right)}^{40}$ is

Find the sum of $3{.}^n{C}_0-8.{}^{n}C_1+13.{}^{n}C_2-18.{}^{n}C_3+\dots \dots \dots .$ upto $(n+1)$ terms.