1) 2
2) 0
3) 1/2
4) 1
Solution: (4) 1
\(\begin{array}{l}\frac{1}{81^{n}}-\frac{10}{81^{n}} 2_{n_{C_{1}}}+\frac{10^{2}}{81^{n}} 2 n_{C_{2}}-\frac{10^{3}}{81^{n}} 2 n_{C_{3}}+\cdots+\frac{10^{2 n}}{81^{n}} \\ =\frac{1}{81^{n}}\left[1-102 n_{C_{1}}+10^{2} 2 n_{C_{2}}-10^{3} 2 n_{C_{3}}+\cdots+10^{2 n}\right]\\ =\frac{1}{81^{n}}(1-10)^{2 n} \\ =\frac{9^{2 n}}{81^{n}}\\=1\end{array} \)
