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cho A=1+1/2+1/3+1/4+.......+1/4026 va B=1+1/3+1/5+........+1/4025
so sanh A/B va 1/2013/2014
Cho A = 1 + 1/2 + 1/3 + 1/4 +...+ 1/4026, B = 1 + 1/3 + 1/5 + 1/7 +...+ 1/4025 So sánh A/B với 1 + 2013/2014
cho A=1+1/2+1/3+1/4+......+1/4026, B=1+1/3+1/5+1/7+...+1/4025 so sanh a/b voi1+2013/2014
Cho A = 1+1/2+1/3+1/4+.....+1/4026 B= 1+1/3+1/5+1/7+....+1/4025. So sánh A/B với 1+2013/2014
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Cho A=1+1/2+1/3+1/4+…+1/4026, B=1+1/3+1/5+1/7+…+1/4025. So sánh A/B với 1+2013/2014
cho A=1+1\2+1\3+...+1\4026,B=1+1\3+1\5+...+1\4025.So sánh A\B và 1\2013\2014
\(\Rightarrow A-B=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{4026}\)
\(B>1+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{4026}=\frac{1}{2}+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{4026}\right)=\frac{1}{2}+\left(A-B\right)\)
\(\Rightarrow B>\frac{1}{2}+\left(A-B\right)\left(1\right)\)
\(A-B=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{4026}< \frac{1}{2}+\frac{1}{2}+...+\frac{1}{2}=\frac{2013}{2}\)
\(\Rightarrow A-B< \frac{2013}{2}\Rightarrow\frac{A-B}{2013}< \frac{1}{2}\left(2\right)\)
Cộng (1) với (2)
\(\Rightarrow\frac{A-B}{2013}+\frac{1}{2}+\left(A-B\right)< \frac{1}{2}+B\Rightarrow\frac{A-B}{2013}+\left(A-B\right)< B\Rightarrow\frac{2014\left(A-B\right)}{2013}< B\Rightarrow\frac{A-B}{B}< \frac{2013}{2014}\)
\(\Rightarrow\frac{A-B}{B}+1< \frac{2013}{2014}+1\Rightarrow\frac{A}{B}< 1\frac{2013}{2014}\left(đpcm\right)\)
Cho A = 1+1/2+1/3+1/4+.....+1/4026 B= 1+1/3+1/5+1/7+....+1/4025
So sánh A với 1+2013/2014
Cho A=1+1/2+1/3+1/4+…+1/4026, B=1+1/3+1/5+1/7+…+1/4025. So sánh A/B với 1+2013/2014
cho a=1+1\2...+z\4026,b=1+1/3+1/5+...+1/4025 so sanh a\b voi1\2013\2014