ĐỀ SAI NHA
Đặt \(A=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)
\(\Rightarrow A=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}.......\frac{99.101+1}{99.101}\)
\(\Rightarrow A=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}..................\frac{10000}{99.101}\)
\(\Rightarrow A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...............\frac{100^2}{99.101}\)
\(\Rightarrow A=\frac{\left(2.3.4..............100\right).\left(2.3.4................100\right)}{\left(1.2.3.................99\right).\left(3.4.5.............101\right)}\)
\(\Rightarrow A=\frac{100.2}{1.101}=\frac{200}{101}=1\frac{99}{101}\)
Vậy \(A=1\frac{99}{101}\)
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