là sao

Ta có: \(\frac{1}{201\times299}+\frac{1}{203\times297}+\cdots+\frac{1}{297\times203}+\frac{1}{299\times201}\)

\(=\frac{2}{201\times299}+\frac{2}{203\times297}+\cdots+\frac{2}{249\times251}\)

\(=\frac{2}{500}\times\left(\frac{500}{201\times299}+\frac{500}{203\times297}+\cdots+\frac{500}{249\times251}\right)\)

\(=\frac{1}{250}\times\left(\frac{1}{201}+\frac{1}{299}+\frac{1}{203}+\frac{1}{297}+\cdots+\frac{1}{249}+\frac{1}{251}\right)\)

\(=\frac{1}{250}\times\left(\frac{1}{201}+\frac{1}{203}+\cdots+\frac{1}{297}+\frac{1}{299}\right)\)

Ta có: \(\frac{\left(\frac{1}{201}+\frac{1}{203}+\cdots+\frac{1}{297}+\frac{1}{299}\right)}{\frac{1}{201\times299}+\frac{1}{203\times297}+\cdots+\frac{1}{297\times203}+\frac{1}{299\times201}}\)

\(=\frac{\left(\frac{1}{201}+\frac{1}{203}+\cdots+\frac{1}{297}+\frac{1}{299}\right)}{\frac{1}{250}\times\left(\left(\frac{1}{201}+\frac{1}{203}+\cdots+\frac{1}{297}+\frac{1}{299}\right)\right)}\)

\(=1:\frac{1}{250}=250\)

203 chia hết cho 7 = 29 

299 chia hết cho  13 = 23

203 chia hết cho 7, 29, 1, 203

299 chia hết cho 13, 23, 299, 1

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

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

\(\Rightarrow\)Có 100 phân số

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

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

             ...................

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

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

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

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y =2436 nha !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!