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Ta có :
\(\frac{2013}{2014}< 1\)( 1 )
\(\frac{2014}{2015}< 1\)( 2 )
\(\frac{2015}{2016}< 1\)( 3 )
từ ( 1 ) , ( 2 ) và ( 3 )
\(\Rightarrow\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2016}< 1+1+1=3\)
vậy A < 3
Có: 2013/2014<2014/2014
2014/2015<2015/2015
2015/2016<2016/2016
=>2013/2014+2014/2015+2015/2016<2014/2014+2015/015+2016/2016
=>A<3
A = \(\frac{2013}{2014}+\frac{2014}{2015}>\frac{1}{2}+\frac{1}{2}=1\)
\(B=\frac{2013+2014+2015}{2014+2015+2016}<1\)
\(Vậy:A>B\)
Đúng nha Nguyễn Bình Minh
so sánh:
\(A=\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2016}\) và\(B=\) \(\frac{2013+2014+2015}{2014+2015+2016}\)
\(B=\frac{2013}{2014+2015+2016}+\frac{2014}{2014+2015+2016}+\frac{2015}{2014+2015+2016}\)
Ta có: \(\frac{2013}{2014}>\frac{2013}{2014+2015+2016}\)
\(\frac{2014}{2015}>\frac{2014}{2014+2015+2016}\)
\(\frac{2015}{2016}>\frac{2015}{2014+2015+2016}\)
\(\Rightarrow\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2016}>\frac{2013+2014+2015}{2014+2015+2016}\)
Vậy: \(A>B\)
Ta có : 1-2014/2017=3/2017
1-2013/2016=3/2016
Vì 3/2017<3/2016 nên 2014/2017>2013/2016
A = 2016^2015 +1 / 2016^2014+1 < 2016^2015 + 1 + 2015 / 2016^2014 + 1 + 2015
= 2016^2015 + 2016 / 2016^2014 + 2016
= 2016(2016^2014 + 1 ) / 2016(2016^2013 +1)
= 2016^2014 + 1 / 2016^2013 + 1 = B
=> A < B
ta có: \(A=\frac{2014^{2013}+1}{2014^{2013}-1}=\frac{2014^{2013}-1+2}{2014^{2013}-1}=1+\frac{2}{2014^{2013}-1}\)
\(B=\frac{2014^{2013}-1}{2014^{2013}-3}=\frac{2014^{2013}-3+2}{2014^{2013}-3}=1+\frac{2}{2014^{2013}-3}\)
\(\Rightarrow\frac{2}{2014^{2013}-1}< \frac{2}{2014^{2013}-3}\)
\(\Rightarrow1+\frac{2}{2014^{2013}-1}< 1+\frac{2}{2014^{2013}-3}\)
=> A < B
Vì 2016>2013.
=>\(\frac{387}{2016}< \frac{387}{2013}\left(1\right)\)
Vì 387>109.
=>\(\frac{387}{2016}>\frac{109}{2016}\left(2\right)\)
Từ (1) và (2),suy ra:
\(\frac{109}{2016}< \frac{387}{2013}\)
Vậy............
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