Question

Cho \(A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.....\frac{79}{80}.CMR\)

\(A<\frac{1}{9}\)

Answer 1

Ta đặt B=\(\frac{2}{3}.\frac{4}{5}...\frac{80}{81}\)

Mà \(\frac{1}{2}<\frac{2}{3};\frac{3}{4}<\frac{4}{5};...;\frac{79}{80}<\frac{80}{81}\)

=>A<B

=>A²<AB=\(\frac{1}{2}.\frac{2}{3}.....\frac{80}{81}=\frac{1}{81}\)

=>A²<\(\frac{1}{81}\)

=>A<\(\sqrt{\frac{1}{81}}=\frac{1}{9}\)(đpcm)

Answer 2

http://olm.vn/hoi-dap/question/419438.html

Answer 3

8/9

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