If $|x| < 1$,then in the expansion of $(1 + 2x + 3x^2 + 4x^3 + ....)^{1/2}$,the coefficient of $x^n$ is

$\frac{1}{4}-\frac{5}{4 \cdot 8}+\frac{5 \cdot 7}{4 \cdot 8 \cdot 12}-\ldots=$

To expand $(1 + 2x)^{-1/2}$ as an infinite series,the range of $x$ should be

If $(a+bx)^{-3} = \frac{1}{27} + \frac{1}{3}x + \dots$,then the ordered pair $(a, b)$ is equal to

For $x>0$,if $p^{\text{th}}$ term is the first negative term in the expansion of $(1+\frac{3x}{5})^{22/3}$ and in the expansion of $(1-\frac{3x}{5})^{22/3}$ from $r^{\text{th}}$ term onwards all the terms are positive,then the number of terms in the expansion of $(px+\frac{r}{x})^{pr}$ is

The cube root of $217$ is: