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\ giải theo pp quy nạp nhé

Đáp án:

Giải thích các bước giải:

\(\frac{A}{B}=\frac{1+\frac{1}{2}+\frac{1}{4}+…+\frac{1}{4026}}{1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4025}}\)

\(=>\frac{A}{B}=\frac{(1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4025})+(\frac{1}{2}+\frac{1}{4}+….+\frac{1}{4026})}{1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4026}}\)

=>\(\frac{A}{B}=\frac{1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4025}}{1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4025}}+\frac{\frac{1}{2}+\frac{1}{4}+….+\frac{1}{4026}}{1+\frac{1}{3}+\frac{1}{5}+…+\frac{1}{4025}}\)

\(=>\frac{A}{B}>1 mà \frac{2013}{2014}<1\)

\(=>\frac{A}{B}>\frac{2013}{2014}\)