\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{20}{21}\)
\(1-\dfrac{1}{x+1}\) \(=\dfrac{20}{21}\)
\(\dfrac{1}{x+1}\) \(=\) \(\dfrac{1}{21}\)
\(=>x+1=21\)
\(x=21-1\)
\(x=20\)
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...\dfrac{1}{x.\left(x+1\right)}=\dfrac{20}{21}\)
\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{20}{21}\)
\(1-\dfrac{1}{x+1}=\dfrac{20}{21}\)
\(\Rightarrow\dfrac{1}{x+1}=\dfrac{20}{21}\)
\(\Leftrightarrow x+1=21\)
\(x=21-1\)
\(x=20\)
Vậy \(x=20\)
