$1+\frac{2}{4}+\frac{2 \cdot 5}{4 \cdot 8}+\frac{2 \cdot 5 \cdot 8}{4 \cdot 8 \cdot 12}+\frac{2 \cdot 5 \cdot 8 \cdot 11}{4 \cdot 8 \cdot 12 \cdot 16}+\ldots \ldots$ 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 sum of the series $1 + \frac{1}{5} + \frac{1 \times 3}{5 \times 10} + \frac{1 \times 3 \times 5}{5 \times 10 \times 15} + \dots$ is equal to

The cube root of $217$ is:

In the expansion of $\frac{2x+1}{(1+x)(1-2x)}$,the sum of the coefficients of the first $5$ odd powers of $x$ is

The sum to infinite terms of the series $\frac{3}{10}+\frac{3 \cdot 7}{10 \cdot 15}+\frac{3 \cdot 7 \cdot 11}{10 \cdot 15 \cdot 20}+\ldots$ to $\infty$ is