Question

tìm x 1/1x2+1/23+1/3x4.....1/Xx(X+1)=1/2

Answer 1

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{2}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{x}{x+1}=\dfrac{1}{2}\)

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow x=1\)