Câu hỏi tương tự nha bạn !

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\(\frac{174}{1313}\)

\(A=13\cdot15+15\cdot17+17\cdot19+...+99\cdot101\)

\(1:A=1:\left(13\cdot15+15\cdot17+...+99\cdot101\right)\)

\(\frac{1}{A}=1:\left(13\cdot15\right)+1:\left(15\cdot17\right)+...+1:\left(99\cdot101\right)\)

\(\frac{1}{A}=\frac{1}{13\cdot15}+\frac{1}{15\cdot17}+...+\frac{1}{99\cdot101}\)

\(\frac{2}{A}=\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+...+\frac{2}{99\cdot101}\)

\(\frac{2}{A}=\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{99}-\frac{1}{101}\)

\(\frac{2}{A}=\frac{1}{13}-\frac{1}{101}\)

\(\frac{2}{A}=\frac{88}{1313}\)

\(A=2:\frac{88}{1313}\)

\(A=\frac{1313}{44}\)

Chắc sai =))

Ta có:

\(A=13.15+15.17+...+99.101\)

\(\Rightarrow\frac{1}{A}=\frac{1}{13.15+15.17+...+99.101}\)

\(=\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{99.101}\)

\(\Rightarrow\frac{1}{A}.2=\frac{1}{2}.A=2.\left(\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{99.101}\right)\)

\(=\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{99.101}\)

\(=\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{99}-\frac{1}{101}\)

\(=\frac{1}{13}-\frac{1}{101}\)

\(=\frac{101-13}{1313}\)

\(=\frac{87}{1313}\)

\(\Rightarrow A=\frac{87}{1313}:\frac{1}{2}=\frac{87}{1313}.2=\frac{174}{1313}\)

Hay wá!!!!!