\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{399}{400}\)
\(2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{399}{400}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{399}{400}:2\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{399}{400}.\frac{1}{2}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{400}{800}-\frac{399}{800}\)
\(\frac{1}{x+1}=\frac{1}{800}\)
\(=>x+1=800\)
\(=>x=800-1=799\)
Vậy x = 799
Ủng hộ mk nha ^_-
