The approximate value of $(1.0002)^{3000}$ is

If $k$ is a positive integer and $10^k$ is a divisor of the number $9^{11}+11^9$,then the greatest value of $k$ is

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

Find the expansion of $(3 x^{2}-2 a x+3 a^{2})^{3}$ using the binomial theorem.

Using the Binomial Theorem,evaluate $(99)^{5}$.

For a real number $r$,let $[r]$ denote the largest integer less than or equal to $r$. Let $a > 1$ be a real number which is not an integer,and let $k$ be the smallest positive integer such that $[a^k] > [a]^k$. Then,which of the following statements is always true?