Find an approximation of $(0.99)^{5}$ using the first three terms of its binomial expansion.

Find $(a+b)^{4}-(a-b)^{4}$. Hence,evaluate $(\sqrt{3}+\sqrt{2})^{4}-(\sqrt{3}-\sqrt{2})^{4}$. (in $\sqrt{6}$)

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

The coefficient of $x^4$ in the expansion of $(1 + x + x^2 + x^3)^n$ is

Let $n$ be a positive integer. Let $A = \sum_{k=0}^{n} (-1)^{k} {}^{n}C_{k} \left[ \left(\frac{1}{2}\right)^{k} + \left(\frac{3}{4}\right)^{k} + \left(\frac{7}{8}\right)^{k} + \left(\frac{15}{16}\right)^{k} + \left(\frac{31}{32}\right)^{k} \right]$. If $63A = 1 - \frac{1}{2^{30}}$,then $n$ is equal to ......

The sum of the coefficients of the terms of degree $m$ in the expansion of $(1 + x)^n(1 + y)^n(1 + z)^n$ is: