Ta có:
\(A=13.15+15.17+...+99.101\)
\(\Rightarrow\frac{1}{A}=\frac{1}{13.15+15.17+...+99.101}\)
\(=\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{99.101}\)
\(\Rightarrow\frac{1}{A}.2=\frac{1}{2}.A=2.\left(\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{99.101}\right)\)
\(=\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{99.101}\)
\(=\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{13}-\frac{1}{101}\)
\(=\frac{101-13}{1313}\)
\(=\frac{87}{1313}\)
\(\Rightarrow A=\frac{87}{1313}:\frac{1}{2}=\frac{87}{1313}.2=\frac{174}{1313}\)
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