Question

3.Tìm X:

2/2.4+2/4.6+....=2/x.(x+2)=4/9

Answer 1

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+2}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x+2-2}{2\left(x+2\right)}=\dfrac{4}{9}\)

\(\Rightarrow\dfrac{x}{2x+4}=\dfrac{4}{9}\)

\(\Rightarrow9x=8x+16\)

\(\Rightarrow x=16\)

Vậy x = 16