cho A = \(\frac{11^{2007}+1}{11^{2008}+1}\)và B = \(\frac{11^{2008}+1}{11^{2009}+1}\). So sánh A và B?
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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 \(A< B\)
ai lam guip toi cau nay voi mai toi nop bai roi
so sanh 2 phan so sau bang cach nahnh nhat: 2007/2008 voi 2008/2009
a) \(A=1-\frac{1}{2008.2009}\) ; \(B=1-\frac{1}{2009.2010}\)
Vì \(\frac{1}{2008.2009}>\frac{1}{2009.2010}\) nên A < B
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