\(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)
\(=\frac{5}{11}-\frac{5}{16}+\frac{5}{16}-\frac{5}{21}+...+\frac{5}{61}-\frac{5}{66}\)
\(=\frac{5}{11}-\frac{5}{66}+0+...+0\)
\(=\frac{25}{66}\)
~ Ủng hộ nhé anh chị em ~
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{21}\)
\(=\frac{1}{11}-\frac{1}{21}\)
\(=\frac{21}{231}-\frac{11}{231}\)
\(=\frac{10}{231}\)
sorry 4 dòng cuối ghi lộn
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{6}{66}-\frac{1}{66}\)
\(=\frac{5}{66}\)
Đặt \(A=\frac{5}{11\times16}+\frac{5}{16\times21}+....+\frac{5}{61\times66}\)
\(A=\frac{16-11}{11\times16}+\frac{21-16}{16\times21}+....+\frac{66-61}{61\times66}\)
\(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{61}-\frac{1}{66}\)
\(\Rightarrow A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)