đặt \(S=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\)
\(2S=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}+\frac{1}{101}\)
\(\Leftrightarrow2S-S=\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{101}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)
\(\Leftrightarrow S=\frac{1}{101}-1=-\frac{100}{101}\)