Theo đề =>\(0,1F=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99,100}\)
\(\Rightarrow0,1F=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow0,1F=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow F=\frac{99}{10}\)
Chúc bạn hc tốt :)