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=1 nhưng mình ko biết trình bày bạn nào làm biết trình bày thì viết hô mình nha ?
Ta có: \(5A=\frac{5^{2011}+5}{5^{2011}+1}=\frac{5^{2011}+1+4}{5^{2011}+1}=1+\frac{4}{5^{2011}+16}\)
\(5B=\frac{5^{2010}+5}{5^{2010}+1}=\frac{5^{2010}+1+4}{5^{2010}+1}=1+\frac{4}{5^{2010}+1}\)
Vì \(\frac{4}{5^{2011}+1}< \frac{4}{5^{2010}+1}\Rightarrow5A< 5B\Rightarrow A< B\)
Ta có:
A = \(\frac{5^{2010}+1}{5^{2011}+1}\)
\(\Rightarrow5A=\frac{5.\left(5^{2010}+1\right)}{5^{2011}+1}\)\(=\frac{5^{2011}+5}{5^{2011}+1}=1+\frac{4}{5^{2011}+1}\)
B=\(\frac{5^{2009}+1}{5^{2010}+1}\)
\(\Rightarrow5B=\frac{5.\left(5^{2009}+1\right)}{5^{2010}+1}=\frac{5^{2010}+5}{5^{2010}+1}=1+\frac{4}{5^{2010}+1}\)
Ta thấy \(5^{2011}+1>5^{2010}+1\)
\(\Rightarrow\frac{4}{5^{2011}+1}< \frac{4}{5^{2010}+1}\)
\(\Rightarrow1+\frac{4}{5^{2011}+1}< 1+\frac{4}{5^{2010}+1}\)
Hay 5.A<5.B
Vậy A<B (đpcm)
\(a)\left(5^{2010}+5^{2012}+5^{2014}\right):\left(5^{2011}+5^{2009}+5^{2007}\right)\)
\(=\dfrac{5^{2007}\left(5^3+5^5+5^7\right)}{5^{2007}\left(5^4+5^2+1\right)}=\dfrac{5^3+5^5+5^7}{5^4+5^2+1}\)
\(=\dfrac{125+3125+78125}{625+25+1}=\dfrac{81375}{651}=125\)
\(b)-\dfrac{7}{45}+\dfrac{1}{4}+\dfrac{3}{5}+\dfrac{1}{12}+\dfrac{2}{3}+\dfrac{1}{39}+\dfrac{5}{9}\)
\(=\dfrac{-7.52+1.585+3.468+1.195+2.780+1.60-5.260}{2340}\)
\(=\dfrac{-364+585+1404+195+1560+60-1300}{2340}\)
\(=\dfrac{2140}{2340}=\dfrac{107}{117}\)
=\(\dfrac{1}{2009.\left(\dfrac{1}{2009}+\dfrac{1}{2011}+\dfrac{1}{2010}\right)}+\dfrac{1}{2010.\left(\dfrac{1}{2010}+\dfrac{1}{2009}+\dfrac{1}{2011}\right)}+\dfrac{1}{2011.\left(\dfrac{1}{2011}+\dfrac{1}{2009}+\dfrac{1}{2010}\right)}\)\(=\dfrac{1}{2009}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2010}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2011}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)\)
\(=\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right):\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)=1\)
Ta có :
\(B=\frac{5^{2009}+1}{5^{2010}+1}=\frac{\left(5^{2009}+1\right).10}{\left(5^{2010}+1\right).10}=\frac{5^{2010}+10}{5^{2011}+10}\)
Ta thấy :
\(5^{2010}=5^{2010};1< 10\Rightarrow5^{2010}+1< 5^{2010}+10\)
\(5^{2011}=5^{2011};1< 10\Rightarrow5^{2011}+1< 5^{2011}+10\)
Suy ra : \(A< B\)
Vậy \(A< B\)
\(A< 1\)
\(A< \frac{5^{2010}+1}{5^{2011}+1}\)
\(A< \frac{5^{2010}+1+4}{5^{2011}+1+4}\)
\(A< \frac{5^{2010}+5}{5^{2011}+5}\)
\(A< \frac{5\left(5^{2009}+1\right)}{5\left(5^{2010}+1\right)}\)
\(A< \frac{5^{2009}+1}{5^{2010}+1}\)
\(A< B\)