Question

so sánh : \(\dfrac{2006^{2006+1}}{2006^{2007+1}}\)và \(\dfrac{2006^{2005+1}}{2006^{2006+1}}\)

Answer 1

Áp dụng Bất đẳng thức :

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

Ta có :

\(\dfrac{2006^{2006}+1}{2006^{2007}+1}< \dfrac{2006^{2006}+1+2005}{2006^{2007}+1+2005}=\dfrac{2006^{2006}+2006}{2006^{2007}+2006}=\dfrac{2006\left(2006^{2005}+1\right)}{2006\left(2006^{2006}+1\right)}=\dfrac{2006^{2005}+1}{2006^{2006}+1}\)

\(\Leftrightarrow\dfrac{2006^{2006}+1}{2006^{2007}+1}< \dfrac{2006^{2005}+1}{2006^{2006}+1}\)