Ta có: \(A=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\cdots+\frac{1}{149\cdot150}\)
\(=1-\frac12+\frac13-\frac14+\cdots+\frac{1}{149}-\frac{1}{150}\)
\(=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{149}+\frac{1}{150}-2\left(\frac12+\frac14+\cdots+\frac{1}{150}\right)\)
\(=1+\frac12+\cdots+\frac{1}{149}+\frac{1}{150}-1-\frac12-.\ldots-\frac{1}{75}\)
\(=\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{150}\)
Ta có: \(\frac{B}{A}=\frac{10\left(\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{150}\right)}{\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{150}}\)
=10
=>B/A là số nguyên
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