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Có :
A = 10 - 9/10^1991+1
B = 10 - 9/10^1992+1
Vì 10^1991+1 < 10^1992+1 => 9/10^1991+1 > 9/10^1992+1
=> A < B
Tk mk nha
\(\frac{A}{10}=\frac{10^{1992}+1}{10^{1992}+10}=\frac{\left(10^{1992}+10\right)-9}{10^{1992}+10}=1-\frac{9}{10^{1992}+10}\)
\(\frac{B}{10}=\frac{10^{1993}+1}{10^{1993}+10}=\frac{\left(10^{1993}+10\right)-9}{10^{1993}+10}=1-\frac{9}{10^{1993}+10}\)
Vì \(10^{1992}+10< 10^{1993}+10\) nên \(1+\frac{9}{10^{1993}+10}>1+\frac{9}{10^{1993}+10}\)
Do đó \(A>B\)
Có: \(B=\frac{10^{1993}+1}{10^{1992}+1}\) Phân tích B thành: \(10^{1993}+1>10^{1992}+1\)
Nên \(B=\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1993}+1+9}{10^{1992}+1+9}\) Và: \(B>\frac{10^{1993}+10}{10^{1992}+10}\)
Hay \(B>\frac{10.\left(10^{1992}+1\right)}{10.\left(10^{1991}+1\right)}\) Mà: \(B>\frac{10^{1992}+1}{10^{1991}+1}=A\) Nên \(B>A\)
Có: B=101993+1101992+1�=101993+1101992+1 Phân tích B thành: 101993+1>101992+1101993+1>101992+1
Nên B=101993+1101992+1>101993+1+9101992+1+9�=101993+1101992+1>101993+1+9101992+1+9 Và: B>101993+10101992+10�>101993+10101992+10
Hay B>10.(101992+1)10.(101991+1)�>10.(101992+1)10.(101991+1) Mà: B>101992+1101991+1=A�>101992+1101991+1=� Nên B>A
Ta viết lại A như sau:
\(A=\frac{10^{1992}+1}{10^{1991}+1}\)
\(=\frac{10^{1991}X10+1}{10^{1991}+1}\)
\(=\frac{10+1}{1}\)
\(=\frac{11}{1}\)
\(=11\)
Ta có :
\(A=\frac{10^{1992}+1}{10^{1991}+1}\)
\(\Rightarrow\frac{1}{10}A=\frac{10^{1992}+1}{10^{1992}+10}=\frac{10^{1992}+10-11}{10^{1992}+10}=1-\frac{11}{10^{1992}+10}\)
\(B=\frac{10^{1993}+1}{10^{1992}+1}\)
\(\Rightarrow\frac{1}{10}B=\frac{10^{1993}+1}{10^{1993}+10}=\frac{10^{1993}+10-11}{10^{1993}+10}=1-\frac{11}{10^{1993}+10}\)
Mà \(10^{1993}+10>10^{1992}+10\)
\(\Rightarrow\frac{11}{10^{1993}+10}< \frac{11}{10^{1992}+10}\)
\(\Rightarrow1-\frac{11}{10^{1993}+10}>1-\frac{11}{10^{1992}+10}\)
\(\Leftrightarrow\frac{1}{10}B>\frac{1}{10}A\)
\(\Rightarrow B>A\)
Ta có : \(B=\frac{10^{1993}+1}{10^{1992}+1}\)< \(\frac{10^{1993}+10}{10^{1992}+10}\) = \(\frac{10.\left(10^{1992}+1\right)}{10.\left(10^{1993}+1\right)}\) = \(\frac{10^{1992}+1}{10^{1991}+1}\) = A
=> B < A
Vậy B < A