So sánh :C=\(\frac{56^{2012}+1}{56^{2013}+1}\)và D=\(\frac{56^{2011}+1}{56^{2012}+1}\)
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b,Ta có
\(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow P>Q\)
\(A=\frac{-10}{20}+\frac{-10}{30}+\frac{-10}{42}+\frac{-10}{56}+\frac{-10}{72}+\frac{-10}{90}+\frac{-10}{110}\)
\(=-10\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\right)\)
\(=-10\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\right)\)
\(=-10\left(\frac{1}{4}-\frac{1}{11}\right)\)
\(=\frac{-35}{22}\)
Ta có :
\(\frac{1}{2013}M=\frac{2013^{2012}+2012}{2013^{2012}+2013}=\frac{2013^{2012}+2013}{2013^{2012}+2013}-\frac{1}{2013^{2012}+2013}=1-\frac{1}{2013^{2012}+2013}\)
Lại có :
\(\frac{1}{2013}N=\frac{2013^{2011}+2012}{2013^{2011}+2013}=\frac{2013^{2011}+2013}{2013^{2011}+2013}-\frac{1}{2013^{2011}+2013}=1-\frac{1}{2013^{2011}+2013}\)
Vì \(\frac{1}{2013^{2012}+2013}< \frac{1}{2013^{2011}+2013}\) nên \(M=1-\frac{1}{2013^{2012}}>N=1-\frac{1}{2013^{2011}+2013}\)
Vậy \(M>N\)
Chúc bạn học tốt ~
\(10A=\frac{2012^{2013}+10}{2012^{2013}+1}=\frac{2012^{2013}+1+9}{2012^{2013}+1}=1+\frac{9}{2012^{2013}+1}\)
\(10B=\frac{2012^{2012}+10}{2012^{2012}+1}=\frac{2012^{2012}+1+9}{2012^{2012}+1}=1+\frac{9}{2012^{2012}+1}\)
Vì \(\frac{9}{2012^{2013}+1}
ta co A=\(\frac{2012^{2012}+1}{2012^{2013}+1}< \frac{2012^{2012}+1+2011}{2012^{2013}+1+2011}\)=\(\frac{2012^{2012}+2012}{2012^{2013}+2012}=\frac{2012\left(2012^{2011}+1\right)}{2012\left(2012^{2012}+1\right)}\)
=>A<B
ÁP DỤNG CÔNG THỨC NẾU \(\frac{a}{b}\)>1 thì
\(\frac{a}{b}\)>\(\frac{a+m}{b+m}\)
Ta có : \(\frac{2012^{12}+1}{2012^{13}+1}\)>\(\frac{2012^{12}+1+2011}{2012^{13}+1+2011}\)=\(\frac{2012^{12}+2012}{2012^{13}+2012}\)=\(\frac{2012.\left(2012^{11}+1\right)}{2012.\left(2012^{12}+1\right)}\)
rồi rút gọn thành \(\frac{2012^{11}+1}{2012^{12}+1}=B\)
Vậy A>B
Nhớ cho mình đúng nha
Ta có:\(A=\dfrac{2012^{2012}+1}{2012^{2013}+1}\)
\(\Rightarrow2012.A=\dfrac{2012^{2013}+2012}{2012^{2013}+1}=\dfrac{2012^{2013}+1+2011}{2012^{2013}+1}=1+\dfrac{2011}{2012^{2013}+1}\)Ta có:\(B=\dfrac{2012^{2011}+1}{2012^{2012}+1}\)
\(\Rightarrow2012.B=\dfrac{2012^{2012}+2012}{2012^{2012}+1}=\dfrac{2012^{2012}+1+2011}{2012^{2012}+1}=1+\dfrac{2011}{2012^{2012}+1}\)Vì\(\dfrac{2011}{2012^{2013}+1}< \dfrac{2011}{2012^{2012}+1}\)
\(\Rightarrow1+\dfrac{2011}{2012^{2013}+1}< 1+\dfrac{2011}{2012^{2012}+1}\)
\(\Rightarrow\dfrac{2012^{2012}+1}{2012^{2013}+1}< \dfrac{2012^{2011}+1}{2012^{2012}+1}\)
Vậy A<B
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,
\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)
xét 56C= \(\dfrac{56\left(56^{2012}+1\right)}{56^{2013}+1}\)=\(\dfrac{56^{2013}+56}{56^{2013}+1}\)=\(1+\dfrac{55}{56^{2013}+1}\)
xét 56D=\(\dfrac{56\left(56^{2011}+1\right)}{56^{2012}+1}\)=\(\dfrac{56^{2012}+56}{56^{2012}+1}\)=\(1+\dfrac{55}{56^{2012}+1}\)
vì \(56^{2013}\)>\(56^{2012}\)
=> \(\dfrac{55}{56^{2013^{ }}+1}\)<\(\dfrac{55}{56^{2012}+1}\)
=>\(1+\dfrac{55}{56^{2013}+1}\)<\(1+\dfrac{55}{56^{2012}+1}\)
=>56C < 56D
=> C <D
tk nha
mình ko chắc nhưng có vẻ C lớn hơn D đó