Question

1/5*8 + 1/ 8* 11+1/11*14+.........+1/26*29

Answer 1

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{26.29}\)

\(=\frac{1}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{26.29}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{29}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{29}\right)\)

\(=\frac{1}{3}.\frac{24}{145}\)

\(=\frac{8}{145}\)

Answer 2

Đặt A=\(\frac{1}{5\times8}+\frac{1}{8\times11}+.......+\frac{1}{26\times29}\)

Ta có: 3A=\(\frac{3}{5\times8}+\frac{3}{8\times11}+....+\frac{3}{26\times29}\)

\(\Rightarrow3A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{26}-\frac{1}{29}\)

\(\Rightarrow3A=\frac{1}{5}-\frac{1}{29}\)

\(\Rightarrow A=\frac{24}{145}:3\)

\(\Rightarrow A=\frac{8}{145}\)

Answer 3

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{26.29}\)

= \(\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}\right)+\frac{1}{3}.\left(\frac{1}{8}-\frac{1}{11}\right)+\frac{1}{3}.\left(\frac{1}{11}-\frac{1}{14}\right)+...+\frac{1}{3}.\left(\frac{1}{26}-\frac{1}{29}\right)\)

= \(\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{29}\right)\)

= \(\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{29}\right)\)

= \(\frac{1}{3}.\frac{24}{145}\)

= \(\frac{8}{145}\)