Question

so sánh

A=\(\frac{2011+2012}{2012+2013}\) và B=\(\frac{2011}{2012}+\frac{2012}{2013}\)

Answer 1

Ta có :

A=\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\left(1\right)\)

B=\(\frac{2011}{2012}+\frac{2012}{2013}\left(2\right)\)

Từ (1) và (2) suy ra A<B

Answer 2

Đầu tiên:

Ta có:

B=\(\frac{2011}{2012+2013}\)+ \(\frac{2012}{2012+2013}\) = \(\frac{2011+2012}{2012+2013}\)

Vì:

\(\frac{2011}{2012+2013}\)< \(\frac{2011}{2012}\); \(\frac{2012}{2012+2013}\)< \(\frac{2012}{2013}\)

\(\Rightarrow\)\(\frac{2011+2012}{2012+2013}\)< \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)

Mà \(\frac{2011+2012}{2012+2013}\)= B; \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)

Vậy B>A