\(\Rightarrow\left[\frac{1}{2\times5}+\frac{1}{5\times8}+...+\frac{1}{17\times20}\right]\cdot\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right]\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\left[\frac{1}{2}-\frac{1}{20}\right]\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\left[\frac{1}{3}\cdot\frac{9}{20}\right]\cdot20=\frac{2x}{10}\)
\(\Rightarrow\frac{3}{20}\cdot20=\frac{2x}{10}\)
\(\Rightarrow3\cdot20=\frac{2x}{10}\Leftrightarrow60=\frac{2x}{10}\)
=> 2x = 60*10
=> 2x = 600
=> x = 300
\(\left(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{340}\right).20=\frac{2x}{10}\)
\(\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\right).20=\frac{2x}{10}\)
\(\left[3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\right].20=\frac{2x}{10}\)
\(\left[3.\left(\frac{1}{2}-\frac{1}{20}\right)\right].20=\frac{2x}{10}\)
\(\left(3.\frac{9}{20}\right).20=\frac{2x}{10}\)
\(\frac{27}{20}.20=2x\div10\)
\(27=2x\div10\)
\(x=27\times10\div2\)
\(\Rightarrow x=135\)
\(\left(\frac{1}{10}+\frac{1}{40}+.....+\frac{1}{340}\right).20=\frac{2x}{10}\)
\(\Leftrightarrow\frac{x}{5}=\left(\frac{1}{2.5}+\frac{1}{5.8}+......+\frac{1}{17.20}\right).20\)
\(\Leftrightarrow\frac{x}{5}=\frac{3}{3}.\left(\frac{1}{2.5}+\frac{1}{5.8}+.....+\frac{1}{17.20}\right).20\)
\(\Leftrightarrow\frac{x}{5}=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+......+\frac{3}{17.20}\right).20\)
\(\Leftrightarrow\frac{x}{5}=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+......+\frac{1}{17}-\frac{1}{20}\right).20\)
\(\Leftrightarrow\frac{x}{5}=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{20}\right).20\)
\(\Leftrightarrow\frac{x}{5}=\frac{1}{3}.\frac{9}{20}.20\)
\(\Leftrightarrow\frac{x}{5}=3\)
\(\Leftrightarrow x=3.5\)
\(\Leftrightarrow x=15\)
