Question

\(CMR:\frac{1}{201}+\frac{1}{202}+....+\frac{1}{399}+\frac{1}{400}>\frac{1}{2}\)

Answer 1

Đặt \(S=\frac{1}{201}+\frac{1}{202}+...+\frac{1}{399}+\frac{1}{400}\)

Ta thấy :

\(\frac{1}{201}>\frac{1}{400}\)

\(\frac{1}{202}>\frac{1}{400}\)

...

\(\frac{1}{399}>\frac{1}{400}\)

\(\Rightarrow S>\frac{1}{400}+\frac{1}{400}+\frac{1}{400}+...+\frac{1}{400}\)

có 200 dãy \(\Rightarrow S>\frac{200}{400}=\frac{1}{2}\)

Vậy : \(S>\frac{1}{2}\)