A=1/2.3/4.5/6.....79/80
CMR: A<1/9
Những câu hỏi liên quan
cho A=1/2.3/4.5/6.7/8.....79/80
CMR: A<1/9
A,Cho S=1/2.3/4.5/6.7/8...99/100
chứng minh rằng S<0,01
b,cho A=1/2.3/4.5/6.7/8...79/80 Chứng minh rằng A<1/9
Cho A = 1/2.3/4.4/5. ... .79/80
CMR A<1/9
CMR :A=1/2.3/4.5/6.....99/100<1/10
đặt \(B=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{98}{99}.\frac{100}{100}\Leftrightarrow A
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A=1/2.3/4.5/6…1999/2000
CMR: A2<1/2001
cho A=1/2.3/4.5/6....199/200. cmr A^2 < 1/201
cho A=1/2.3/4.5/6.../99/100
cmr: 1/15<A<1/10
choA=1/2.3/4.5/6.../99/100. cmr: 1/15<A<1/10
cmr 1/2.3/4.5/6. ... .99/100 < 1/10
A=1/2*3/4*..*99/100
=>A<2/3*4/5*6/7*...*100/101
=>A^2<2/3*4/5*...*100/101*1/2*3/4*...*99/100
=>A^2<1/101<1/100
=>A<1/10
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\(A=\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\)
\(A< \left(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\right).\left(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{6}{7}...\dfrac{98}{99}\right)\)
\(\Rightarrow A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}.\dfrac{5}{6}.\dfrac{6}{7}...\dfrac{98}{99}.\dfrac{99}{100}\)
\(\Leftrightarrow A=\dfrac{1.2.3.4.5.6...98.99}{2.3.4.5.6.7...99.100}\)
\(\Rightarrow A< \dfrac{1}{100}< \dfrac{1}{10}\)
Vậy \(A< \dfrac{1}{10}\)
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