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