Question

Bài 3: Chứng tỏ rằng:

a, Nếu A= \(\dfrac{\left(10^{1990}+1\right)}{10^{1991}+1}\)và B = \(\dfrac{\left(10^{1991}+1\right)}{10^{1992}+1}\)thì A > B

Giúp mik vs! Thanks nha!

Answer 1

Giải:

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

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 : 

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

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

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

\(10B=1+\dfrac{9}{10^{1992}+1}\) 

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

\(\Rightarrow A>B\left(đpcm\right)\) 

Chúc bạn học tốt!