\(\frac{2}{3\cdot7}+\frac{2}{7\cdot11}+...+\frac{2}{71\cdot75}+\frac{2}{75\cdot79}\)
\(=\frac{2}{4}\left[\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+...+\frac{4}{71\cdot75}+\frac{4}{75\cdot79}\right]\)
\(=\frac{2}{4}\left[\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{75}-\frac{1}{79}\right]\)
\(=\frac{1}{2}\left[\frac{1}{3}-\frac{1}{79}\right]=\frac{38}{237}\)
\(\frac{2}{3\cdot7}+\frac{2}{7\cdot11}+...+\frac{2}{71\cdot75}+\frac{2}{75\cdot79}\)
\(=\frac{1}{2}\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+...+\frac{4}{71\cdot75}+\frac{4}{75\cdot79}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{71}-\frac{1}{75}+\frac{1}{75}-\frac{1}{79}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{79}\right)\)
\(=\frac{1}{2}\cdot\frac{76}{237}\)
\(=\frac{38}{237}\)
#)Giải :
Đặt \(A=\frac{2}{3.7}+\frac{2}{7.11}+\frac{2}{11.15}+...+\frac{2}{75.79}\)
\(\Rightarrow2A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{75.79}\)
\(\Rightarrow2A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{75}-\frac{1}{79}\)
\(\Rightarrow2A=\frac{1}{3}-\frac{1}{79}\)
\(\Rightarrow2A=\frac{76}{237}\)
\(\Rightarrow A=\frac{38}{237}\)
đat A=cần tính
\(\Rightarrow2A=\frac{4}{3.7}+\frac{4}{7.11}+.....+\frac{4}{75.79}\)
\(\Rightarrow2A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-....-\frac{1}{79}=\frac{1}{3}-\frac{1}{79}=\frac{76}{237}\Rightarrow A=\frac{38}{237}\)
Đặt \(A=\frac{2}{3.7}+\frac{2}{7.11}+...+\frac{2}{71.75}+\frac{2}{75.79}\)
\(2A=\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{71.75}+\frac{4}{75.79}\)
\(2A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{71}-\frac{1}{75}+\frac{1}{75}-\frac{1}{79}\)
\(2A=\frac{1}{3}-\frac{1}{79}\)
\(2A=\frac{76}{327}\)
\(A=\frac{76}{327}:2=\frac{38}{327}\)
