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Ta có : \(A=\frac{11^{2007}+1}{11^{2008}+1}=\frac{11\left[11^{2007}+1\right]}{11^{2008}+1}=\frac{11^{2008}+11}{11^{2008}+1}=\frac{11^{2008}+1+10}{11^{2008}+1}=1+\frac{10}{11^{2008}+1}\)
\(B=\frac{11^{2008}+1}{11^{2009}+1}=\frac{11\left[11^{2008}+1\right]}{11^{2009}+1}=\frac{11^{2009}+11}{11^{2009}+1}=\frac{11^{2009}+1+10}{11^{2009}+1}=1+\frac{10}{11^{2009}+1}\)
Đến đây bạn tự so sánh nhé
Ta có: B = 11^2008+1/11^2009+1 < 11^20087 +1 + 10/11^2009+1+10 = 11^2008+11/11^2009+11 = 11(11^2007 +1)/11(11^2008+1) = 11^2007 +1/11^2008+1 = A
=>B <A
Vậy A > B
A=\(\frac{2007^{2007}}{2008^{2008}}\)
B=\(\frac{2008^{2008}}{2009^{2009}}\)
\(A=\left(1-\frac{1}{10}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{12}\right)...\left(1-\frac{1}{2007}\right)\left(1-\frac{1}{2008}\right)\)
\(=\frac{9}{10}.\frac{10}{11}.\frac{11}{12}.....\frac{2006}{2007}.\frac{2007}{2008}\)
\(=\frac{9.10.11.....2006.2007}{10.11.12.....2007.2008}\)
\(=\frac{9}{2008}\)
\(Ta\) \(có:\)
\(A=\frac{9}{2008}\)
\(B=\frac{1}{2000}\)
\(\frac{9}{2008}=\frac{9.250}{2008.250}=\frac{2250}{502000}\)
\(\frac{1}{2000}=\frac{1.251}{2000.251}=\frac{251}{502000}\)
Vì \(\frac{2250}{502000}>\frac{251}{502000}\Rightarrow A>B\)
\(A=\left(1-\frac{1}{10}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{12}\right)...\left(1-\frac{1}{2007}\right)\left(1-\frac{1}{2008}\right)\)
\(A=\frac{9}{10}.\frac{10}{11}.\frac{11}{12}....\frac{2006}{2007}.\frac{2007}{2008}\)
\(A=\frac{9.10.11....2006.2007}{10.11.12...2007.2008}\)
\(A=\frac{9}{2008}\)
Vì \(\frac{9}{2008}
Sửa lại:
Ta có: \(A=\frac{11^{2007}+1}{11^{2008}+1}\Rightarrow11A=\frac{11^{2008}+11}{11^{2008}+1}=1+\frac{10}{11^{2008}+1}\)
\(B=\frac{11^{2008}+1}{11^{2009}+1}\Rightarrow11B=\frac{11^{2009}+11}{11^{2009}+1}=1+\frac{10}{11^{2009}+1}\)
Vì \(\frac{10}{2^{2008}+1}>\frac{10}{11^{2009}+1}\Rightarrow1+\frac{10}{2^{2008}+1}>1+\frac{10}{11^{2009}+1}\)
\(\Rightarrow11A>11B\)
\(\Rightarrow A>B\)
Ta có: \(A=\frac{11^{2007}+1}{11^{2008}+1}\)
\(\Rightarrow11A=\frac{11^{2008}+11}{11^{2008}+1}=1+\frac{10}{11^{2008}+1}\)
\(B=\frac{11^{2008}+1}{11^{2009}+1}\)
\(\Rightarrow11B=\frac{11^{2009}+11}{11^{2009}+1}=1+\frac{10}{11^{2009}+1}\)
Vì \(\frac{10}{11^{2008}+1}< \frac{10}{11^{2009}+1}\Rightarrow1+\frac{10}{11^{2008}+1}< 1+\frac{10}{11^{2009}+1}\)
\(\Rightarrow11A< 11B\)
\(\Rightarrow A< B\)
Vậy \(A< B\)