Ta thấy:
\(\frac{1}{201}>\frac{1}{400}\)
\(\frac{1}{202}>\frac{1}{400}\)
............................
\(\frac{1}{399}>\frac{1}{400}\)
\(\frac{1}{400}=\frac{1}{400}\)
Cộng theo vế ta được:
\(\frac{1}{201}+\frac{1}{202}+...+\frac{1}{400}>\frac{1}{400}+\frac{1}{400}+....+\frac{1}{400}=\frac{200}{400}=\frac{1}{2}\)
\(\frac{1}{201}+\frac{1}{202}+...+\frac{1}{400}>\frac{1}{400}.200=\frac{1}{2}\)
Vậy
\(\frac{1}{201}+\frac{1}{202}+......+\frac{1}{399}+\frac{1}{400}>\frac{1}{2}\)
\(\Rightarrow\left(400-201\right):+1=200\)
\(\Rightarrow\frac{1}{400}.200=\frac{200}{400}=\frac{1}{2}\)
\(\Rightarrow\frac{1}{2}< \frac{1}{201}+......+\frac{1}{400}\)
