\(\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{19.20.21}\right).x=5\)
\(\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{21-19}{19.20.21}\right).x=5\)
\(\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{19.20}-\frac{1}{20.21}\right).x=5\)
\(\left(\frac{1}{1.2}-\frac{1}{20.21}\right).x=5\)
\(\frac{209}{420}.x=5\)
\(\Rightarrow x=5\div\frac{209}{420}=\frac{2100}{209}\)
\(\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{19.20.21}\right).x=5\)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{19.20.21}\right).2.x=5\)
\(\left(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{19.20}-\frac{1}{20.21}\right)\right).x.2=5\)
\(\left(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{19.20}-\frac{1}{20.21}\right)\right).x=5\div2\)
\(\left(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{20.21}\right)\right).x=2,5\)
\(\left(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{420}\right)\right).x=2,5\)
\(\left(\frac{1}{2}\times\frac{209}{420}\right)\times x=2,5\)
\(\frac{209}{840}\times x=2,5\)
\(x=2,5\div\frac{209}{840}=10\frac{10}{209}\)
