Question

1\(\frac{1}{12}-\frac{1}{20}-...-\frac{1}{380}=?\)

Answer 1

\(\frac{1}{12}-\frac{1}{20}-...-\frac{1}{380}\)

\(=\frac{1}{3.4}-\frac{1}{4.5}-...-\frac{1}{19.20}\)

\(=\left(\frac{1}{3}-\frac{1}{4}\right)-\left(\frac{1}{4}-\frac{1}{5}\right)-\left(\frac{1}{5}-\frac{1}{6}\right)-...-\left(\frac{1}{19}-\frac{1}{20}\right)\)

\(=\frac{1}{3}-\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-...-\frac{1}{19}+\frac{1}{20}\)

\(=\frac{1}{3}-\frac{1}{4}-\frac{1}{4}+\frac{1}{20}\)

\(=-\frac{7}{60}\)