Question

Cho M= 2012^37+37^2012+1/2012^38 và N= 2012^38+37^2012+2/2012^39. So sánh M và N

Answer 1

Ta có :M=\(\frac{2012^{37}+37^{2012}+1}{2012^{38}}\)=\(\frac{1}{2012}\)+\(\frac{37^{2012}}{2018^{38}}\)+\(\frac{1}{2012^{38}}\)

N=\(\frac{2012^{38}+37^{2012}+2}{2012^{39}}\)=\(\frac{1}{2012}\)+\(\frac{37^{2012}}{2012^{39}}\)+\(\frac{2}{2012^{39}}\)

Suy ra: M-N=\(\frac{37^{2012}}{2012^{38}}\left(1-\frac{1}{2012}\right)\)+\(\frac{1}{2012^{38}}\left(1-\frac{2}{2012}\right)\)

\(\Rightarrow\)M-N=\(\frac{37^{2012}}{2012^{38}}.\frac{2011}{2012}+\frac{1}{2012^{38}}.\frac{2010}{2012}\)

\(\Rightarrow\)M-N>0

\(\Rightarrow\)M>N

Vậy M>N