Question

A = - 1/20 - 1/30 - 1/42 - 1/56 - 1/72 - 1/90

Answer 1

\(A=-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}-\dfrac{1}{56}-\dfrac{1}{72}-\dfrac{1}{90}\)

\(\Rightarrow-A=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

\(\Rightarrow-A=\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\)

\(\Rightarrow-A=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(\Rightarrow-A=\dfrac{1}{4}-\dfrac{1}{10}\)

\(\Rightarrow-A=\dfrac{3}{20}\)

\(\Rightarrow A=-\dfrac{3}{20}\)

Vậy \(\ A=-\dfrac{3}{20}\)