cho A=1+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{4026},B=1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{4025}\)so sanh \(\frac{A}{B}\)voi\(1\frac{2013}{2014}\)
Những câu hỏi liên quan
cho \(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{4026},B=1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{4025}\)so sanh \(\frac{A}{B}\)voi \(1\frac{2013}{2014}\)
Cho A = 1+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{4026}\) ; B = \(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{4025}\) . So sánh \(\frac{A}{B}với1\frac{2013}{2014}\)
Cho A = 1+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{4026}\) ; B = \(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{4025}\) . So sánh \(\frac{A}{B}với1\frac{2013}{2014}\)
Cho A=1+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{4026}\)
B=1+\(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{4025}\)
So sánh \(\frac{A}{B}vs1\frac{2013}{2014}\)
Ta có
\(\frac{A}{B}=\frac{1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{4026}}{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}\)
\(\Rightarrow\frac{A}{B}=\frac{\left(1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}\right)+\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{4026}\right)}{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}\)
\(\Rightarrow\frac{A}{B}=\frac{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}+\frac{\frac{1}{2}+\frac{1}{4}+....+\frac{1}{4026}}{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}\)
\(\Rightarrow\frac{A}{B}=1+\frac{\frac{1}{2}+\frac{1}{4}+....+\frac{1}{4026}}{1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{4025}}\)
Dễ thấy A/B > 1
2013/2014<1
=> \(\frac{A}{B}>\frac{2013}{2014}\)
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Bình luận (5)
Cho \(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{4026},B=1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{4025}\) . So sánh \(\frac{A}{B}=1\frac{2013}{2014}\)
Cho A= \(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{4026}\)
B= \(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+.....+\frac{1}{4025}\)
So sánh \(\frac{A}{B}\)và \(1\frac{2013}{2014}\)
Cho A=\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{4026}\)
B=\(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{4025}\)
So sánh \(\frac{A}{B}\) và \(1\frac{2013}{2014}\)
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Cho A=\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{4026}\) , B=\(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{4025}\). So sánh \(\frac{A}{B}\) với \(1\frac{2013}{2014}\)
Cho \(A=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{4026}\)
\(B=1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{4025}\)
So sánh \(\frac{A}{B}\)với \(1\frac{2013}{2014}\)