2.
The sum \(\displaystyle \frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\ldots+\frac{2022}{2023!}\) Can be expressed as \(\displaystyle a-\frac{1}{b!}\), where \(a\) and \(b\) are positive integers. What is \(a-b\)？
[提示]
\(\displaystyle \frac{k}{(k+1)!}=\frac{k+1}{(k+1)!}-\frac{1}{(k+1)!}=\frac{1}{k!}-\frac{1}{(k+1)!}\)
我的教甄準備之路 裂項相消，
https://math.pro/db/viewthread.php?tid=661&page=2#pid1678
6.
Among the 900 three-digit numbers from 100 to 999, how many of them the sum of the three digits is smaller than 15？
