Question

tìm x biết;

2/2*4+2/4*6+...+2/x*(x+2)=4/9

cố gắng giúp mình nhanh nhanh nha

Answer 1

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

\(\dfrac{4-2}{2.4}+\dfrac{6-4}{4.6}+...+\dfrac{\left(x+2\right)-x}{x\left(x+2\right)}=\dfrac{4}{9}\)

\(\dfrac{4}{2.4}-\dfrac{2}{2.4}+\dfrac{6}{4.6}-\dfrac{4}{4.6}+...+\dfrac{x+2}{x\left(x+2\right)}-\dfrac{x}{x\left(x+2\right)}=\dfrac{4}{9}\)

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

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

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

\(\dfrac{1}{x+2}=\dfrac{1}{18}\Rightarrow x+2=18\Rightarrow x=16\)

Vậy x = 16