\(\dfrac{4}{6.8}+\dfrac{4}{8.10}+...+\dfrac{4}{40.42}\)
\(=2\left(\dfrac{2}{6.8}+\dfrac{2}{8.10}+...+\dfrac{2}{40.42}\right)\)
\(=2\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{42}\right)\)
\(=2\left(\dfrac{1}{6}-\dfrac{1}{42}\right)\)
\(=2.\dfrac{1}{7}\)
\(=\dfrac{2}{7}\)
Cho \(A=\dfrac{4}{6.8}+\dfrac{4}{8.10}+...+\dfrac{4}{40.42}\)
\(2A=\dfrac{2}{6.8}+\dfrac{2}{8.10}+...+\dfrac{2}{40.42}\)
\(2A=\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{42}\)
\(2A=\dfrac{1}{6}-\dfrac{1}{42}\)
\(2A=\dfrac{1}{7}\)
\(A=\dfrac{1}{7}:2\)
\(A=\dfrac{1}{14}\)
