If $|x| < 1$,then the coefficient of $x^n$ in the expansion of $(1 + x + x^2 + ....)^2$ will be

The coefficient of $x^3$ in the power series expansion of $\frac{1+4x-3x^2}{(1+3x)^3}$ is

If $|x|$ is so small that $x^2$ and higher powers of $x$ may be neglected, then the approximate value of $\frac{\sqrt{4+x}+\sqrt[3]{8-x}}{\left(1-\frac{2x}{3}\right)^{\frac{3}{2}}}$ when $x=\frac{6}{25}$ is

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

Find the binomial expansion of $\frac{1}{\sqrt[3]{6 - 3x}}$.

If $x > \sqrt{3}$ and $\frac{x^2+1}{(x^2+2)(x^2+3)}$ is expanded in terms of powers of $x^{-2}$,then the coefficient of $x^{-8}$ is