Nhân 2 bên với 4 được:
\(4E=\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{95\cdot99}\)
\(4E=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\)
\(4E=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
\(E=\frac{\frac{32}{99}}{4}=\frac{8}{99}\)
Bg
Ta có: E = \(\frac{1}{3\times7}+\frac{1}{7\times11}+\frac{1}{11\times15}+...+\frac{1}{95\times99}\)
=> E = \(\frac{1}{4}\times\left(\frac{4}{3\times7}+\frac{4}{7\times11}+\frac{4}{11\times15}+...+\frac{4}{95\times99}\right)\)
=> E = \(\frac{1}{4}\times\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\right)\)
=> E = \(\frac{1}{4}\times\left(\frac{1}{3}-\frac{1}{99}\right)\)
=> E = \(\frac{1}{4}\times\left(\frac{33}{99}-\frac{1}{99}\right)\)
=> E = \(\frac{1}{4}\times\frac{32}{99}\)
=> E = \(\frac{8}{99}\)
