\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{499}{999}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{499}{999}\div2\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{499}{1998}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{250}{999}\)
\(\Leftrightarrow\left(x+1\right).250=999\Rightarrow x+1=\frac{999}{250}\Rightarrow x=\frac{999}{250}-1=\frac{749}{250}\)
Như kiểu đề sai hay sao ý