The expression $\frac{1}{\sqrt{5 + 4x}}$ can be expanded by the binomial theorem,if

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

If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \dots \infty$,then

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

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

If the $(r + 1)^{th}$ term is the first negative term in the expansion of $(1 + x)^{7/2}$,then the value of $r$ is