Question

Tìm x biết :

\(\frac{10}{1\times2}+\frac{10}{2\times3}+...+\frac{10}{x\times\left(x+1\right)}=9\)

Answer 1

\(\Leftrightarrow10\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{x\times\left(x+1\right)}\right)=9\)

\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right)=9\div10\)

\(\Leftrightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\)

\(\Leftrightarrow\frac{1}{x+1}=1-\frac{9}{10}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{10}\)

\(\Rightarrow x+1=10\)

\(\Leftrightarrow x=9\)

Vậy x = 9