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a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)
Ta có chính chất phân số trung gian là \(\frac{2^{10}+1}{2^{10}-3}\)
\(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}\) ; \(\frac{2^{10}-1}{2^{10}-3}< \frac{2^{10}+1}{2^{10}-3}\)
Vì \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}>\frac{2^{10}-1}{2^{10}-3}\)
Nên \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}-1}{2^{10}-3}\)
b) \(A=\frac{2011}{2012}+\frac{2012}{2013}\)và \(B=\frac{2011+2012}{2012+2013}\)
Ta có : \(A=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}=B\)
Vậy A > B
Có gì sai cho sorry
a,
\(\frac{2^{10}+1}{2^{10}-1}=1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}=\frac{2^{10}-1}{2^{10}-3}\)
b,
\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)
a)
\(10A=\frac{10^{2002}+10}{10^{2002}+1}=1+\frac{9}{10^{2002}+1}\)
\(10B=\frac{10^{2003}+10}{10^{2003}+1}=1+\frac{9}{10^{2003}+1}\)
=> 10A > 10B => A > B
Áp dụng a/b < 1 => a/b < a+m/b+m (a,b,m thuộc N*)
\(=>B=\frac{10^{2012}+1}{10^{2013}+1}< \frac{10^{2012}+1+9}{10^{2013}+1+9}\)
\(< \frac{10^{2012}+10}{10^{2013}+10}\)
\(< \frac{10.\left(10^{2011}+1\right)}{10.\left(10^{2012}+1\right)}\)
\(< \frac{10^{2011}+1}{10^{2012}+1}=A\)
=> B < A
Ủng hộ mk nha ^_-
Bài 2:1-2+3-4+...+2011-2012
=1+2+3+4+...+2011+2012-2(2+4+6+...+2012)
=2025078-2(1012036)
=2025078-2024072
=1006
Học giỏi!
Có : \(A=\frac{10^{2012}-10}{10^{2013}-10}\)
\(\Leftrightarrow10A=\frac{10^{2013}-100}{10^{2013}-10}\)
\(\Leftrightarrow10A=\frac{10^{2013}-10-90}{10^{2013}-10}\)
\(\Leftrightarrow10A=1-\frac{90}{10^{2013}-10}\)
Có : \(B=\frac{10^{2011}+10}{10^{2012}+10}\)
\(\Leftrightarrow10B=\frac{10^{2012}+100}{10^{2012}+10}\)
\(\Leftrightarrow10B=\frac{10^{2012}+10+90}{10^{2012}+10}\)
\(\Leftrightarrow B=1+\frac{90}{10^{2012}+10}\)
Ta thấy : \(1-\frac{90}{10^{2013}-10}< 1\)
\(1+\frac{90}{10^{2012}+10}>1\)
\(\Leftrightarrow1-\frac{90}{10^{2013}-10}< 1+\frac{90}{10^{2012}+10}\)
\(\Leftrightarrow A< B\)
So sánh 2 phân số sau $\frac{10^{2011}+10}{10^{2012}+10}v\text{à}\frac{10^{2012}-10}{10^{2013}-10}$102011+10102012+10 và102012−10102013−10
kick dzô chữ xanh là được!! OK
Ta có :
10. A = \(\frac{10.\left(10^{2011}+1\right)}{10^{2012}+1}\)
= \(\frac{10^{2012}+10}{10^{2012}+1}\)
= \(\frac{10^{2012}+1+9}{10^{2012}+1}\)
= \(\frac{10^{2012}+1}{10^{2012}+1}-\frac{9}{10^{2012}+1}\)
= 1 - \(\frac{9}{10^{2012}+1}\)
10 . B = \(\frac{10.\left(10^{2012}+1\right)}{10^{2013}+1}\)
= \(\frac{10^{2013}+10}{10^{2013}+1}\)
= \(\frac{10^{2013}+1+9}{10^{2013}+1}\)
= 1 - \(\frac{9}{10^{2013}+1}\)
Vì \(\frac{9}{10^{2012}+1}\) >\(\frac{9}{10^{2013}+1}\) nên 10.A > 10.B
=> A >B
Vậy ...........