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godofsong 發表於 2023-6-8 10:49

112北陽明高中雙語數學試題

如題

bugmens 發表於 2023-6-9 09:10

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]
\(\displaystyle \frac{k}{(k+1)!}=\frac{k+1}{(k+1)!}-\frac{1}{(k+1)!}=\frac{1}{k!}-\frac{1}{(k+1)!}\)
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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?

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