Question

Answer 1

Lời giải:

a. 

\(A=\frac{10(10^{1991}+1)-9}{10^{1991}+1}=10-\frac{9}{10^{1991}+1}\)

\(B=\frac{10(10^{1992}+1)-9}{10^{1992}+1}=10-\frac{9}{10^{1992}+1}\)

Mà: \(\frac{9}{10^{1991}+1}> \frac{9}{10^{1992}+1}\Rightarrow A< B\)

b.

\(10C=\frac{2010^{2009}+1+9}{2010^{2009}+1}=1+\frac{9}{2010^{2009}+1}\)

\(10D=\frac{2010^{2008}+1+9}{2010^{2008}+1}=1+\frac{9}{2010^{2008}+1}\)

Mà: \(\frac{9}{2010^{2009}+1}< \frac{9}{2010^{2008}+1}\Rightarrow \Rightarrow 10C< 10D\Rightarrow C< D\)