\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{46.51}\)
\(=\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{46.51}\right)\)
\(=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{46}-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\left(1-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\left(\frac{51}{51}-\frac{1}{51}\right)\)
\(=\frac{1}{5}.\frac{50}{51}\)
\(=\frac{10}{51}\)
Chúc bạn học tốt !!!
Đặt \(A=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{46\cdot51}\)
\(5A=5\left(\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{46\cdot51}\right)\)
\(5A=\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{46\cdot51}\)
\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{46}-\frac{1}{51}\)
\(5A=1-\frac{1}{51}\)
\(5A=\frac{50}{51}\Rightarrow A=\frac{50}{51}:5\Rightarrow A=\frac{10}{51}\)
