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AK
8 tháng 5 2018
Ta có :
\(\frac{2015}{2016}>\frac{2015}{2016+2017}\)
\(\frac{2016}{2017}>\frac{2016}{2016+2017}\)
\(\Rightarrow\frac{2015}{2016}+\frac{2016}{2017}>\frac{2015+2016}{2016+2017}\)
\(\Rightarrow A>\frac{2015+2016}{2016+2017}\)
\(\Rightarrow A>B\)
Chúc bạn học tốt !!!
8 tháng 5 2018
\(A=\frac{2015}{2016}+\frac{2016}{2017}\) \(B=\frac{2015+2016}{4033}\)
\(A=\frac{2015}{2016}+\frac{2016}{2017}\) \(B=\frac{2015}{4033}+\frac{2016}{4033}\)
\(\Rightarrow A>B\)
ND
3
5 tháng 2 2017
Vì 20162016 + 1 < 20162017 + 1
\(\Rightarrow\frac{2016^{2016}+1}{2016^{2017}+1}< \frac{2016^{2016}+1+2015}{2016^{2016}+1+2015}=\frac{2016^{2016}+2016}{2016^{2017}+2016}=\frac{2016\left(2016^{2015}+1\right)}{2016\left(2016^{2016}+1\right)}\)
\(=\frac{2016^{2015}+1}{2016^{2016}+1}=B\)
\(\Rightarrow\)A < B
5 tháng 2 2017
Ta có :
\(A=\frac{2016^{2016}+1}{2016^{2017}+1}< \frac{2016^{2016}+2015+1}{2016^{2017}+2015+1}=\frac{2016^{2016}+2016}{2016^{2017}+2016}=\frac{2016.\left(2016^{2015}+1\right)}{2016.\left(2016^{2016}+1\right)}\)
\(=\frac{2016^{2015}+1}{2016^{2016}+1}=B\)
\(\Rightarrow A< B\)
4 tháng 5 2017
\(A=\frac{100^{2007}+1}{100^{2008}+1}\Rightarrow100.A=\frac{100^{2008}+100}{100^{2008}+1}=\frac{100^{2008}+1+99}{100^{2008}+1}=1+\frac{99}{100^{2008}+1}\)
\(B=\frac{100^{2006}+1}{100^{2007}+1}\Rightarrow100.B=\frac{100^{2007}+100}{100^{2007}+1}=\frac{100^{2007}+1+99}{100^{2007}+1}=1+\frac{99}{100^{2007}+1}\)
Vì \(\frac{99}{100^{2007}+1}>\frac{99}{100^{2008}+1};1=1\Rightarrow1+\frac{99}{100^{2007}+1}>1+\frac{99}{100^{2008}+1}\)hay \(A>B\)
Vậy \(A>B\)
NT
2
19 tháng 4 2015
\(10A=\frac{10^{2015}+1+9}{10^{2015}+1}=1+\frac{9}{10^{2015}+1}\)
\(10B=\frac{10^{2017}+1+9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)
Vì \(\frac{9}{10^{2015}+1}>\frac{9}{10^{2017}+1}\Rightarrow10A>10B\Rightarrow A>B\)
LX
0
\(\frac{a}{b}=\frac{a\left(b+2015\right)}{b\left(b+2015\right)}=\frac{ab+2015a}{b\left(b+2015\right)}\)
\(\frac{a+2015}{b+2015}=\frac{b\left(a+2015\right)}{b\left(b+2015\right)}=\frac{ab+2015b}{b\left(b+2015\right)}\)
TH1: a = b
=> ab+2015a = ab+2015b
=> \(\frac{a}{b}=\frac{a+2015}{b+2015}\)
TH2: a > b
=> ab+2015a > ab+2015b
=> \(\frac{a}{b}>\frac{a+2015}{b+2015}\)
TH3: a < b
=> ab+2015a < ab+2015b
=> \(\frac{a}{b}<\frac{a+2015}{b+2015}\)
Ta có:\(\frac{a}{b}=\frac{a.\left(b+2015\right)}{b.\left(b+2015\right)}=\frac{ab+a.2015}{b.\left(b+2015\right)}\)
\(\frac{a+2015}{b+2015}=\frac{b.\left(a+2015\right)}{b.\left(b+2015\right)}=\frac{ab+b.2015}{b.\left(b+2015\right)}\)
Xét a>b=>a.2015>b.2015
=>\(\frac{ab+a.2015}{b.\left(b+2015\right)}>\frac{ab+b.2015}{b.\left(b+2015\right)}\)
=>\(\frac{a}{b}>\frac{a+2015}{b+2015}\)
Xét a=b=>a.2015=b.2015
=>\(\frac{ab+a.2015}{b.\left(b+2015\right)}=\frac{ab+b.2015}{b.\left(b+2015\right)}\)
=>\(\frac{a}{b}=\frac{a+2015}{b+2015}\)
Xét a<b=>a.2015<b.2015
=>\(\frac{ab+a.2015}{b.\left(b+2015\right)}<\frac{ab+b.2015}{b.\left(b+2015\right)}\)
=>\(\frac{a}{b}<\frac{a+2015}{b+2015}\)
Vậy \(\frac{a}{b}>\frac{a+2015}{b+2015}\)khi a>b
\(\frac{a}{b}=\frac{a+2015}{b+2015}\)khi a=b
\(\frac{a}{b}<\frac{a+2015}{b+2015}\)khi a<b