Question

[Nam Vũ Tú]

Cho A =\(\dfrac{100^{2007}+1}{100^{2008}+1}\) và B = \(\dfrac{100^{2006}+1}{100^{2007+1}}\).Hãy so sánh A và B

Answer 1

[Nguyễn Thanh Hằng]

Áp dụng tính chất : \(\dfrac{a}{b}< 1\Leftrightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\) (\(a;b,m\in N\)*)

Ta có :

\(A=\dfrac{100^{2007}+1}{100^{2008}+1}< \dfrac{100^{2007}+1+99}{100^{2008}+1+99}=\dfrac{100^{2007}+100}{100^{2008}+100}=\dfrac{100\left(100^{2006}+1\right)}{100\left(100^{2007}+1\right)}=\dfrac{100^{2006}+1}{100^{2007}+1}=B\)

\(\Rightarrow A< B\)