Question

So sánh 2 biểu thức A và B biết:

A=\(\dfrac{10^{2007}+1}{10^{2008}+1}\)

B=\(\dfrac{10^{2008}+1}{10^{2009}+1}\)

Answer 1

Cách 2:

Ta có: \(10A=\dfrac{10^{2008}+10}{10^{2008}+1}=1+\dfrac{9}{10^{2008}+1}\)

\(10B=\dfrac{10^{2009}+10}{10^{2009}+1}=1+\dfrac{9}{10^{2009}+1}\)

Vì \(\dfrac{9}{10^{2008}+1}>\dfrac{9}{10^{2009}+1}\Rightarrow1+\dfrac{9}{10^{2008}+1}>1+\dfrac{9}{10^{2009}+1}\)

\(\Rightarrow10A>10B\Rightarrow A>B\)

Vậy A > B

Answer 2

A<B

Answer 3

Ta có :
\(B=\dfrac{10^{2008}+1}{10^{2009}+1}< \dfrac{10^{2008}+1+9}{10^{2009}+1+9}\)
Biến đổi vế trái:
\(\dfrac{10^{2008}+10}{10^{2009}+10}\)= \(\dfrac{10.\left(10^{2007}+1\right)}{10.\left(10^{2008}+1\right)}\)= \(\dfrac{10^{2007}+1}{10^{2008}+1}\)= A
Suy ra:
A > B.