Question

[Nguyễn Thảo Chi]

So sánh \(\frac{37^{2013}+1}{37^{2012}+1}\) và\(\frac{37^{2014}+1}{37^{2013}+1}\)

Answer 1

[Phùng Minh Quân]

Đặt \(A=\frac{37^{2013}+1}{37^{2012}+1}\) và \(B=\frac{37^{2014}+1}{37^{2013}+1}\) ta có : 

\(\frac{1}{37}A=\frac{37^{2013}+1}{37^{2013}+37}=\frac{37^{2013}+37-36}{37^{2013}+37}=\frac{37^{2013}+37}{37^{2013}+37}-\frac{36}{37^{2013}+37}=1-\frac{36}{37^{2013}+37}\)

\(\frac{1}{37}B=\frac{37^{2014}+1}{37^{2014}+37}=\frac{37^{2014}+37-36}{37^{2014}+37}=\frac{37^{2014}+37}{37^{2014}+37}-\frac{36}{37^{2014}+37}=1-\frac{36}{37^{2014}+37}\)

Vì \(\frac{36}{37^{2013}+37}>\frac{36}{37^{2014}+37}\) nên \(1-\frac{36}{37^{2013}+37}< 1-\frac{36}{37^{2014}+37}\)

\(\Rightarrow\)\(\frac{1}{37}A< \frac{1}{38}B\)

\(\Rightarrow\)\(A< B\)

Vậy \(A< B\)

Chúc bạn học tốt ~ 

Answer 2

[Ongniel]

\(A< B\)

Chúc bạn học tốt\(\approx\)