So Sánh \(A=\frac{10^{2006+1}}{10^{2007}+1}\) và \(\frac{10^{2007}+1}{10^{2008}+1}\)
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so sánh
A=\(\frac{10^{2006}+1}{10^{2007}+1}\)và B=\(\frac{10^{2007}+1}{10^{2008}+1}\)
HEPL ME TO
Áp dụng \(\frac{a}{b}< 1\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\)(\(a;b;m\in\)N*)
Ta có:
\(B=\frac{10^{2007}+1}{10^{2008}+1}< \frac{10^{2007}+1+9}{10^{2008}+1+9}\)
\(B< \frac{10^{2007}+10}{10^{2008}+10}\)
\(B< \frac{10.\left(10^{2006}+1\right)}{10.\left(10^{2007}+1\right)}\)
\(B< \frac{10^{2006}+1}{10^{2007}+1}=A\)
=> \(B< A\)
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so sánh A và B
\(A=\frac{10^{2006}+1}{10^{2007}+1}\) \(B=\frac{10^{2007}+1}{10^{2008}+1}\)
So sánh A và B biết
A=\(\frac{10^{2006}+1}{10^{2007}+1}\);B=\(\frac{10^{2007}+1}{10^{2008}+1}\)
So sánh: \(\frac{10^{2006}+1}{10^{2007}+1}\)và \(\frac{10^{2007}+1}{10^{2008}+1}\)
Đặt A=\(\frac{10^{2006}+1}{10^{2007}+1}\);\(B=\frac{10^{2007}+1}{10^{2008}+1}\)
10A=\(\frac{10\left(10^{2006}+1\right)}{10^{2007}+1}\)=\(\frac{10^{2007}+1+9}{10^{2007}+1}\)
10B=\(\frac{10\left(10^{2007}+1\right)}{10^{2008}+1}=\frac{10^{2008}+1+9}{10^{2008}+1}\)
Vì \(\frac{9}{10^{2007}+1}>\frac{9}{10^{2008}+1}\)nên 10A>10B nên A>B
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A=\(\frac{10^{2006}+1}{10^{2007}+1}\) và B=\(\frac{10^{2007}+1}{10^{2008}+1}\)
Hãy so sánh A và B
\(1-A=\frac{10^{2007}-10^{2006}}{10^{2007}+1}=\frac{9.10^{2006}}{10^{2007}+1}=\frac{9.2^{2007}}{10^{2008}+10}\)
\(1-B=\frac{10^{2008}-10^{2007}}{10^{2008}+1}=\frac{9.10^{2007}}{10^{2008}+1}\)
=>1-A< 1-B
=> A > B
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So sánh A và B biết : \(A=\dfrac{10^{2006}+1}{10^{2007}+1},B=\dfrac{10^{2007}+1}{10^{2008}+1}\)
so sánh A và B
\(A=\frac{10^{2006}+1}{10^{2007}+1}\) \(B=\frac{10^{2007}+1}{10^{2008}+1}\)
So sánh a=10^2006+1/10^2007+1 VÀ B=10^2007+1/10^2008+1
Hãy so sánh A và B , biết:A=10^2006+1/10^2007+1;B=10^2007+1 / 10^2008+1
10A=10*\(\frac{10^{2006}+1}{10^{2007}+1}\) 10B=10*\(\frac{10^{2007}+1}{10^{2008}+1}\)
10A=\(\frac{10^{2007}+1+9}{10^{2007}+1}\) 10B=\(\frac{10^{2008}+1+9}{10^{2008}+1}\)
10A=1+\(\frac{9}{10^{2007}+1}\) 10B=1+\(\frac{9}{10^{2008}+1}\)
Vì \(\frac{9}{10^{2007}+1}\)>\(\frac{9}{10^{2008}+1}\)=>1+\(\frac{9}{10^{2007}+1}\)>1+\(\frac{9}{10^{2008}+1}\)
Nên 10A>10B=>A>B
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Ta có: \(A=\frac{10^{2006}+1}{10^{2007}+1}\)
\(=>10A=\frac{10^{2007}+10}{10^{2007}+1}=\frac{10^{2007}+1+9}{10^{2007}+1}=\frac{10^{2007}+1}{10^{2007}+1}+\frac{9}{10^{2007}+1}=1+\frac{9}{10^{2007}+1}\)
\(B=\frac{10^{2007}+1}{10^{2008}+1}\)
\(=>10B=\frac{10^{2008}+10}{10^{2008}+1}=\frac{10^{2008}+1+9}{10^{2008}+1}=\frac{10^{2008}+1}{10^{2008}+1}+\frac{9}{10^{2008}+1}=1+\frac{9}{10^{2008}+1}\)
Vì \(10^{2007}+1< 10^{2008}+1=>\frac{9}{10^{2007}+1}>\frac{9}{10^{2008}+1}=>1+\frac{9}{10^{2007}+1}>1+\frac{9}{10^{2008}+1}=>10A>10B=>A>B\)
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Cho B = \(\frac{10^{2007}+1}{10^{2008}+1}\)
Rõ ràng B < 1 nên theo B, nếu \(\frac{a}{b}< 1\) thì \(\frac{a+n}{b+n}>\frac{a}{b}\) => B < \(\frac{\left(10^{2007}+1\right)+9}{\left(10^{2008}+1\right)+9}=\frac{10^{2007}+10}{10^{2008}+10}\)
Do đó B < \(\frac{10^{2007}+10}{10^{2008}+10}=\frac{10\left(10^{2006}+1\right)}{10\left(10^{2007}+1\right)}=\frac{10^{2006}+1}{10^{2007}+1}\)
=> A > B
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