$1+\frac{1}{3}+\frac{1 \times 3}{3 \times 6}+\frac{1 \times 3 \times 5}{3 \times 6 \times 9}+\ldots \text{ to } \infty =$

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

If $x$ is so small that $x^5$ and higher powers of $x$ may be neglected,then the coefficient of $x^4$ in the expansion of $\sqrt{x^2+4}-\sqrt{x^2+9}$ is

If $x$ is so small that $x^2$ and higher powers of $x$ can be neglected,then the approximate value of $\left(1+\frac{3}{4} x\right)^{\frac{1}{2}}\left(1-\frac{2 x}{3}\right)^{-2}$ is

In the expansion of $\left(1+\frac{3x}{2}\right)^{-5}$,the coefficient of $x^{10}$ is equal to the coefficient of $x^{10}$ in $(1+ax)^n$,where $n \in N$. Then $na$ is equal to:

The coefficient of $x^3$ in the expansion of $(1-2x)^{1/2}(1+3x)^{-1/3}$ is