Question

So sánh:

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

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

Answer 1

Ta có :

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

\(10B=\dfrac{10^{1992}+10}{10^{1992}+1}=\dfrac{10^{1992}+1+9}{10^{1992}+1}=1+\dfrac{9}{10^{1992}+1}\)\(\left(2\right)\)

Vì \(1+\dfrac{9}{10^{1991}+1}>1+\dfrac{9}{10^{1992}+1}\)\(\left(3\right)\)

Từ \(\left(1\right)+\left(2\right)+\left(3\right)\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

~ Chúc bn học tốt ~

Answer 2

Ta có:

A=101990+1101991+1=101990.10101991.10=101990101991=1/10A=101990+1101991+1=101990.10101991.10=101990101991=1/10 (%)

B=101991+1101992+1=101991.10101992.10=101991101992=1/10B=101991+1101992+1=101991.10101992.10=101991101992=1/10 (%) (%)

Answer 3

Ta có B=\(\dfrac{10^{1991}+1}{10^{1992}+1}\)<\(\dfrac{10^{1991}+1+9}{10^{1992}+1+9}\)=\(\dfrac{10^{1991}+10}{10^{1992}+10}\)=\(\dfrac{10.\left(10^{1990}+1\right)}{10.\left(10^{1991}+1\right)}\)=\(\dfrac{10^{1990}+1}{10^{1991}+1}\)=A

Vậy B<A