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 \(\dfrac{2013}{2014}\)

a = 1+ 1/2 +1/3+...+1/ 1025 + 1/1026

a= 1+ (1/12+1/3+....+1/1025) - (1/2+1/3+...+1/1025+ 1/1026)

a= 1+ (1/2- 1/1026)

a= 1+ 256/513

a= 283/171

ko chắc chắn

đúng k nha

Ta có:

AB=1+1/2+1/3+...+1/4026/1+1/3+1/5+1/7+...+1/4025

⇒AB=(1+1/3+1/5+...+1/4025)+(1/2+1/4+...+1/2046)1+1/3+1/5+...+1/4025

⇒AB=1+1/3+1/5+...+1/4025/1+1/3+1/5+....+1/4025+1/2+1/4+...+1/4026/1+1/3+1/5+...+1/4025

⇒AB=1+1/2+1/4+...+1/2046/1+1/3+1/5+...+1/4025

Dễ thấy AB>1

Mà 20132014<1

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