107 The 100th digit after the decimal point of the number $(\sqrt{5}+2)^{1997}$ is
A. 0
B. 1
C. 2
D. Greater than 2
107 A. $(\sqrt{5}+2)^{1997}-(\sqrt{5}-2)^{1997}$ is an integer. Therefore, the decimal parts of $(\sqrt{5}+2)^{1997}$ and $(\sqrt{5}-2)^{1997}$ are exactly the same. And $(\sqrt{5}-2)^{1997}<(\sqrt{5}-2)^{200}<0.3^{200}<0.1^{100}$. So the 100th digit after the decimal point of $(\sqrt{5}+2)^{1997}$ is 0.