Ta có :
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+....+\frac{4}{23.27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+....+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}==\frac{9}{27}-\frac{1}{27}=\frac{8}{27}\)
Đặt \(A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}++\frac{4}{19.23}+\frac{4}{23.27}\)
\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{23}-\frac{1}{27}\)
\(A=\frac{1}{3}-\frac{1}{27}\)
\(A=\frac{8}{27}\)
\(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+\frac{4}{15\cdot19}+\frac{4}{19\cdot23}+\frac{4}{23.27}\)
\(=\frac{4}{4}\cdot\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\right)\)
\(=\frac{4}{4}\cdot\left(\frac{1}{3}-\frac{1}{27}\right)\)
\(=\frac{4}{4}\cdot\frac{8}{27}=\frac{8}{27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)(. là dấu nhân )
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{8}{27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{23}-\frac{1}{23}\right)-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{9}{27}-\frac{1}{27}\)
\(=\frac{8}{27}\)
\(a.\frac{4}{3x7}+\frac{4}{7x11}+\frac{4}{11x15}+\frac{4}{15x19}+\frac{4}{19x23}+\frac{4}{23x27}\)
\(a.\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}\)
\(a.\frac{1}{3}-\frac{1}{23}\)
\(a.\frac{23}{69}-\frac{3}{69}\)
\(a.\frac{20}{69}\)
mình cảm ơn các bạn rất nhiều nhé
thank
