\(M=\frac{7}{1.3}+\frac{7}{3.5}+...+\frac{7}{91.93}\)
\(=\frac{7}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{91.93}\right)\)
\(=\frac{7}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{91}-\frac{1}{93}\right)\)
\(=\frac{7}{2}\left(1-\frac{1}{93}\right)=\frac{7}{2}.\frac{92}{93}=\frac{332}{93}\)
suy ra 2/7*M = 2/1*3 +2/3*5 +2/5*7 +.......+2/91*93
suy ra 2/7*M= 1-1/3 +1/3 -1/5 +1/5 -1/7 + .....+ 1/91 - 1/93
suy ra 2/7*M= 1-1/93=92/93
suy ra M= 92/93 : 2/7= 322/93
Vay M = 322/93
\(giải:\)
\(M=\frac{7}{1.3}+\frac{7}{3.5}+...+\frac{7}{91.93}\)
\(=7\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{91.93}\right)\)
\(=\frac{7}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{91.93}\right)\)
\(=\frac{7}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{91}-\frac{1}{93}\right)\)
\(=\frac{7}{2}\left(1-\frac{1}{93}\right)\)
\(=\frac{7}{2}.\frac{92}{93}\)
\(=\frac{322}{93}\)
Ta có : \(M=\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+.....+\frac{7}{91.93}\)
\(\Rightarrow\frac{2}{7}M=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{91.93}\)
\(\Rightarrow\frac{2}{7}M=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{91}-\frac{1}{93}\)
\(\Rightarrow\frac{2}{7}M=1-\frac{1}{93}\)
\(\Rightarrow\frac{2}{7}M=\frac{92}{93}\)
\(\Rightarrow M=\frac{92}{93}.\frac{7}{2}=\frac{322}{93}\)