Sửa đề:
\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{x\times\left(x+1\right)}=\frac{9}{10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(1-\frac{1}{x}=\frac{9}{10}\)
\(\frac{1}{x}=1-\frac{9}{10}=\frac{1}{10}\)
Vậy, x = 10.
Ko bt có right ko?
Nhầm.
Chuyển \(1-\frac{1}{x}\)thành \(1-\frac{1}{x+1}\)
\(1-\frac{1}{x+1}=\frac{9}{10}\)
\(\frac{1}{x+1}=1-\frac{9}{10}=\frac{1}{10}\)
Vậy x = 10 - 1 = 9
Thế ms right chứ!
\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\Leftrightarrow\frac{1}{x+1}=\frac{1}{1}-\frac{9}{10}=\frac{1}{10}\)
\(\Leftrightarrow x+1=10\Rightarrow x=10-1=9\)
Vậy x = 9