$\dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + ... + \dfrac{1}{x(x+1)} = \dfrac{20}{21} (x \neq 0; x\neq -1)$
⇔ $\dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{4} + ... + \dfrac{1}{x} - \dfrac{1}{x+1} = \dfrac{20}{21}$
⇔ $1 - \dfrac{1}{x+1} = \dfrac{20}{21}$
⇔ $\dfrac{x + 1 - 1}{x + 1} = \dfrac{20}{21}$
⇔ $\dfrac{x}{x + 1} = \dfrac{20}{21}$
⇒ $21x = 20(x+1)$
⇔ $21x - 20x = 20$
⇔ $x = 20 (T/m)$