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\(M=\left(1-\frac{1}{2}\right)-\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{6}\right)-....-\left(1-\frac{1}{200}\right)\)
\(M=-\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{6}-.....-\frac{1}{200}\right)=-\frac{1}{2}\left(1-\frac{1}{2}+...-\frac{1}{100}\right)\)
Xét:
\(S=1-\frac{1}{2}+....-\frac{1}{100}.S=\left(1+\frac{1}{2}+...+\frac{1}{100}\right)-2\left(\frac{1}{2}+....+\frac{1}{100}\right)=\frac{1}{51}+...+\frac{1}{100}\)
\(\Rightarrow M=-\frac{1}{2}\left(\frac{1}{51}+....+\frac{1}{100}\right)\)
N:M=-2
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
=> \(\frac{A}{B}>\frac{2013}{2014}\)
\(1\dfrac{2013}{2014}\) cơ mà sao lại \(\dfrac{2013}{2014}\)
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gửi lắm thế m