\(\dfrac{1}{3.7}\)+\(\dfrac{1}{7.4}\) +\(\dfrac{1}{4.9}\) +...+\(\dfrac{2}{x\left(x+1\right)}\) =\(\dfrac{2}{9}\)
\(\dfrac{2}{2.3.7}\)+\(\dfrac{2}{2.7.4}\) +\(\dfrac{2}{2.4.9}\) +...+\(\dfrac{2}{x\left(x+1\right)}\) =\(\dfrac{2}{9}\)
\(\dfrac{2}{6.7}\)+\(\dfrac{2}{7.8}\) +\(\dfrac{2}{8.9}\) +...+\(\dfrac{2}{x\left(x+1\right)}\) =\(\dfrac{2}{9}\)
2(\(\dfrac{1}{6.7}\) +\(\dfrac{1}{7.8}\) +\(\dfrac{1}{8.9}\) +...+\(\dfrac{1}{x\left(x+1\right)}\)) =\(\dfrac{2}{9}\)
2(\(\dfrac{1}{6}\) -\(\dfrac{1}{7}\) +\(\dfrac{1}{7}\) -\(\dfrac{1}{8}\) +\(\dfrac{1}{8}\) -\(\dfrac{1}{9}\) +...+\(\dfrac{1}{x}\)-\(\dfrac{1}{x+1}\) ) =\(\dfrac{2}{9}\)
2(\(\dfrac{1}{6}\) -\(\dfrac{1}{x+1}\) )=\(\dfrac{2}{9}\)
\(\dfrac{1}{6}\)-\(\dfrac{1}{x+1}\) =\(\dfrac{2}{9}\) : 2
\(\dfrac{1}{6}\)-\(\dfrac{1}{x+1}\) =\(\dfrac{1}{9}\)
\(\dfrac{1}{x+1}\) = \(\dfrac{1}{6}\) -\(\dfrac{1}{9}\)
\(\dfrac{1}{x+1}\) = \(\dfrac{1}{18}\)
x+1=18
x = 18-1
x =17
Vậy x =17
