1/201>1/300,1/202>1/300.................1/300=1/300 =>S>1/300.100=1/3                                                 1/201<1/200, 1/202<1/300.................1/300<1/200=>S<1/200.100=1/2

a: Ta có: \(\frac{1}{201}>\frac{1}{400};\frac{1}{202}>\frac{1}{400};\ldots;\frac{1}{400}=\frac{1}{400}\)

Do đó: \(\frac{1}{201}+\frac{1}{202}+\cdots+\frac{1}{400}>\frac{1}{400}+\frac{1}{400}+\cdots+\frac{1}{400}\)

=>\(\frac{1}{201}+\frac{1}{202}+\cdots+\frac{1}{400}>\frac{200}{400}=\frac12\)

b: Ta có: \(\frac{1}{201}<\frac{1}{200};\frac{1}{202}<\frac{1}{200};\ldots;\frac{1}{400}<\frac{1}{200}\)

Do đó: \(\frac{1}{201}+\frac{1}{202}+\cdots+\frac{1}{400}<\frac{1}{200}+\frac{1}{200}+\cdots+\frac{1}{200}\)

=>\(\frac{1}{201}+\frac{1}{202}+\cdots+\frac{1}{400}<\frac{200}{200}=1\)

\(M=\frac{1}{201}+\frac{1}{202}+...+\frac{1}{299}+\frac{1}{300}\)

\(\Rightarrow\)Có 100 phân số

Ta có: \(\frac{1}{201}>\frac{1}{300}\)

          \(\frac{1}{202}>\frac{1}{300}\)

             ...................

            \(\frac{1}{299}>\frac{1}{300}\)

            \(\frac{1}{300}=\frac{1}{300}\)

\(\Rightarrow M>\left(\frac{1}{300}+\frac{1}{300}+...+\frac{1}{300}\right)=\frac{100}{300}=\frac{1}{3}\)

Vậy....

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