If the number of terms in the binomial expansion of $(2x + 3)^{3n}$ is $22$,then the value of $n$ is:

What is the sum of the coefficients of $(x^2 - x - 1)^{99}$?

The coefficient of $x^{101}$ in the expression $(5+x)^{500} + x(5+x)^{499} + x^{2}(5+x)^{498} + \ldots + x^{500}$ for $x > 0$ is:

When $|x| < 2$,the coefficient of $x^2$ in the power series expansion of $\frac{x}{(x-2)(x-3)}$ is

If $|x|$ is so small that all terms containing $x^2$ and higher powers of $x$ can be neglected,then the approximate value of $\frac{(3-5x)^{1/2}}{(5-3x)^2}$,when $x=\frac{1}{\sqrt{363}}$,is

The number of non-zero terms in the expansion of $(1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9$ is