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$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
Đặt phân thức trên là D
=> D=(1+1+1+1+...+1+2013/2+2012/3+...+2/2013+1/2014)/(1/2+1/3+1/4+...+1/2014)
=> D=(1+2013/2+1+2012/3+1+2011/4+...+1+2/2013+1+1/2014+1)/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=(2015/2+2015/3+2015/4+...+2015/2013+2015/2014+1)/(1/2+1/3+1/4+...+1/2014)
=> D=[2015*(1/2+1/3+1/4+1/5+....+1/2014)]/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=2015
D=2013+2014/ 2014+2015
D= 2013/2014+2015 + 2014/2014+2015
2013/2014+2015 < 2013/2014
2014/2014+2015 < 2014/2015
suy ra 2013/2014+2015 +2014/2014+2015 < 2013/2014+ 2014/2015
hay D < C ( ĐPCM)
XONG NHA BẠN !@!!!!!!!!!!!!!!!!!!!!chắc chắn đúng lun
a)\(\frac{2013}{2015}< \frac{2014}{2016}\)
b)\(\frac{2013+2014}{2014+2015}< \frac{2013}{2014}+\frac{2014}{2015}\)
tớ cần gấp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Ta có 1+1/2014 +1/x=1/(x+1)+1+1/2013 nên 1/x-1/(x+1)=1/2013-1/(2013+1) nên x=2013
Ta có: \(\frac{1}{x}-\frac{1}{x+1}=\frac{2014}{2013}-\frac{2015}{2014}\)
<=> \(\frac{1}{x\left(x+1\right)}=\frac{2014^2-2015.2013}{2013.2014}=\frac{1}{2013.2014}\)
<=> x(x+1)=2013.2014
=> x=2013
Đáp số: x=2013
Ta có:
\(\frac{2013}{2014}>\frac{2013}{2014+2015}\)
\(\frac{2014}{2015}>\frac{2014}{2014+2015}\)
=> \(\frac{2013}{2014}+\frac{2014}{2015}>\frac{2013}{2014+2015}+\frac{2014}{2014+2015}\)
=> \(\frac{2013}{2014}+\frac{2014}{2015}>\frac{2013+2014}{2014+2015}\)
TS :
3 + 5 + 7 + ... + 2015
SSH là : ( 2015 - 3 ) : 2 + 1 = 1007 ( số )
Tổng là : ( 2015 + 3 ) . 1007 : 2 = 4064252
→Vì TS : MS = 1 => TS = MS
Ta có : 2 + 4 + 6 + ... + 2014 + x = 4 064 252
2 + 4 + 6 + ... + 2014 = 4 064 252 - x
SSH ở vế trái là : ( 2014 - 2 ) : 2 + 1 = 1007 ( số )
Tổng là : ( 2014 + 2 ) . 1007: 2 = 4 060 224
Vậy x là : 4 064 252 - 4 060 224 = 4028
Vậy x là 4028
Có: \(A=\frac{1}{2013}x\frac{2015}{2014}-\frac{2014}{2013}\)
\(=\frac{1}{2013}.\frac{2015}{2014}-\frac{1}{2013}.2014=\frac{1}{2013}.\left(\frac{2015}{2014}-2014\right)\)
Thế A bằng bao nhiêu