Question

Tính 

 \(1-\frac{1}{90}-\frac{1}{72}-\frac{1}{52}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

Answer 1

\(1-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=1-\left(\frac{1}{90}+\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)

\(=1-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)

\(=1-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)

\(=1-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=1-\left(1-\frac{1}{10}\right)\)

\(=1-\frac{9}{10}\)

\(=\frac{1}{10}\)