Question

So sánh:

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

Answer 1

đáng ra là toán lớp 6 đó nhưng mik thích đặt toán lớp 5 :)

 

Answer 2

A = \(\dfrac{10^{1990}+1}{10^{1991}+1}\) ⇒ 10A = \(\dfrac{10^{1991}+10}{10^{1991}+1}\) = \(1+\dfrac{9}{10^{1991}+1}\)

B =  \(\dfrac{10^{1991}+10}{10^{1992}+1}\) ⇒ 10B = \(\dfrac{10^{1992}+10}{10^{1992}+1}\) = 1 + \(\dfrac{9}{10^{1992}+1}\)

Vì \(\dfrac{9}{10^{1991}+1}\) > \(\dfrac{9}{10^{1992}+1}\)

10A > 10B => A > B