Question

Tìm x, biết: A=\(\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x.\left(x+1\right)}=\dfrac{4}{5}\)

Answer 1

\(A=\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x.\left(x+1\right)}=\dfrac{4}{5}\)

⇒ \(A=2.\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x.\left(x+1\right)}\right)=\dfrac{4}{5}\)

⇒ \(A=2.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}\right)=\dfrac{4}{5}\)

⇒\(A=2.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{4}{5}\)

⇒\(A=\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{4}{5}:2=\dfrac{2}{5}\)

⇒\(A=\dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{2}{5}=\dfrac{1}{10}\)

⇒x+1 = 10

⇒ x = 10 - 1

⇒ x = 9