\(M=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{946}+\frac{1}{990}\right)\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1892}+\frac{1}{1980}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{43.44}+\frac{1}{44.45}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{43}-\frac{1}{44}+\frac{1}{44}-\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}M=\frac{1}{5}-\frac{1}{45}=\frac{9}{45}-\frac{1}{45}=\frac{8}{45}\)
\(\Rightarrow M=\frac{8}{45}:\frac{1}{2}=\frac{8}{45}.2=\frac{16}{45}\)
nhớ ấn đúng cho mình nha
\(M=\frac{2}{30}+\frac{2}{42}+...+\frac{2}{1980}\)
\(=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{44}-\frac{1}{45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=2\times\frac{8}{45}\)
\(=\frac{16}{45}\)
\(M=2\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+..+\frac{1}{1980}\right)\)
\(=2\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{44.45}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=\frac{16}{45}\)