Question

so sánh \(\dfrac{10^{1990}+1}{10^{1991}+1}\)và \(\dfrac{10^{1991}}{10^{1992}}\)

Answer 1

Giải:

Ta gọi \(\dfrac{10^{1990}+1}{10^{1991}+1}\) =A và \(\dfrac{10^{1991}}{10^{1992}}\) =B

Ta có:

A=\(\dfrac{10^{1990}+1}{10^{1991}+1}\) 

10A=\(\dfrac{10^{1991}+10}{10^{1991}+1}\) 

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

10A=\(1+\dfrac{9}{10^{1991}+1}\) 

Tương tự:

B=\(\dfrac{10^{1991}}{10^{1992}}\) 

10B=\(\dfrac{10^{1992}}{10^{1992}}=1\) 

Vì \(\dfrac{9}{10^{1991}+1}< 1\) nên 10A<10B

⇒ \(\dfrac{10^{1990}+1}{10^{1991}+1}\) < \(\dfrac{10^{1991}}{10^{1992}}\)