\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
Tính
\(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{17}{34}-\frac{2}{34}=\frac{15}{34}\)
Ta có: Biểu thức trên sẽ =
\(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)1/17 (nó bị lỗi nên k viết đc T_T)
= \(\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
Chúc bạn học tốt!~
ủa sao lại viết đc rồi nhỉ? khó hiểu
Ta có: \(\frac{3}{2\cdot5}=\frac{5-2}{2\cdot5}=\frac{5}{2\cdot5}-\frac{2}{2\cdot5}=\frac{1}{2}-\frac{1}{5}\)
Tương tự: \(\frac{3}{5\cdot8}=\frac{1}{5}-\frac{1}{8}\)
...
\(\frac{3}{14\cdot17}=\frac{1}{14}-\frac{1}{17}\)
\(\Rightarrow\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+...+\frac{3}{14\cdot17}=\left(\frac{1}{2}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{8}\right)+...+\left(\frac{1}{14}-\frac{1}{17}\right)\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-...-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+...+\left(\frac{1}{14}-\frac{1}{14}\right)-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\\\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}\)
\(=\frac{15}{34}\)