Question

So sánh A=\(\frac{10^{2011}+1}{10^{2012}+1}\)và B=\(\frac{10^{2012}+1}{10^{2013}+1}\)

Answer 1

\(B< \frac{10^{2012}+1+9}{10^{2013}+1+9}=\frac{10^{2012}+10}{10^{2013}+10}=\frac{10\left(10^{2011}+1\right)}{10\left(10^{2012}+1\right)}=\frac{10^{2011}+1}{10^{2012}+1}=A\)

Vậy A > B

Answer 2

Áp dụng bất đẳng thức :

\(\frac{a}{b}< 1\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\)

Ta có :

\(B=\frac{10^{2012}+1}{10^{2013}+1}< \frac{10^{2012}+1+9}{10^{2013}+1+9}=\frac{10^{2012}+10}{10^{2013}+10}=\frac{10\left(10^{2011}+1\right)}{10\left(10^{2012}+1\right)}=\frac{10^{2011}+1}{10^{2012}+1}=A\)

\(\Leftrightarrow B< A\)

Answer 3

cảm ơn nhiều