\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{11}{40}\)
\(\Leftrightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{11}{40}\div2\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{11}{80}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{16}\Rightarrow x=16-1=15\)
