So sánh : A=\(\frac{2013^{2012}+1}{2013^{2013}+1}\) với B=\(\frac{2013^{2013}+1}{2013^{2014}+1}\)
so sánh giá trị A và B với
\(A=\frac{2013^{2014}+1}{2013^{2015}+1};\)\(B=\frac{2013^{2012}+1}{2013^{2013}+1}\)
1) So sánh : \(A=\frac{2013^{2012}+1}{2013^{2013}+1}\)
\(B=\frac{2013^{2013}+1}{2013^{2014}+1}\)
bài toán này 92% người được huy chương vàng toán làm sai
Ta có:\(2013A=\frac{2013\left(2013^{2012}+1\right)}{2013^{2013}+1}=\frac{2013^{2013}+2013}{2013^{2013}+1}=\frac{2013^{2013}+1+2012}{2013^{2013}+1}=\frac{2013^{2013}+1}{2013^{2013}+1}+\frac{2012}{2013^{2013}+1}=1+\frac{2012}{2013^{2013}+1}\)
\(2013B=\frac{2013\left(2013^{2013}+1\right)}{2013^{2014}+1}=\frac{2013^{2014}+2013}{2013^{2014}+1}=\frac{2013^{2014}+1+2012}{2013^{2014}+1}=\frac{2013^{2014}+1}{2013^{2014}+1}+\frac{2012}{2013^{2014}+1}=1+\frac{2012}{2013^{2014}+1}\)
Vì 20132013+1<20132014+1
\(\Rightarrow\frac{2012}{2013^{2013}+1}>\frac{2012}{2013^{2014}+1}\)
\(\Rightarrow1+\frac{2012}{2013^{2013}+1}>1+\frac{2012}{2013^{2014}+1}\)
\(\Rightarrow2013A>2013B\)
\(\Rightarrow A>B\)
HCV cái jề. lấy 2013 lm nhân tử chung, b cx z là dc
so sánh
C=\(\frac{2013^{2013}+1}{2013^{2014}+1}\)
D=\(\frac{2013^{2012+1}}{2013^{2013}+1}\)
\(C=\frac{2013^{2013}+1}{2013^{2014}+1}\Rightarrow2013C=\frac{2013^{2014}+2013}{2013^{2014}+1}=\frac{2013^{2014}+1+2012}{2013^{2014}+1}=1+\frac{2012}{2013^{2014}+1}\)
\(D=\frac{2013^{2012}+1}{2013^{2013}+1}\Rightarrow2013D=\frac{2013^{2013}+2013}{2013^{2013}+1}=\frac{2013^{2013}+1+2012}{2013^{2013}+1}=1+\frac{2012}{2013^{2013}+1}\)
=>\(1+\frac{2012}{2013^{2014}+1}<1+\frac{2012}{2013^{2013}+1}\)
=>2013C<2013D
=>C<D
C = 20132013+ 1 / 20132014+1 < 20132013+1+2012 / 20132014+1+2012
= 20132013+2013 / 20132014+2013
= 2013(20132012+1) / 2013(20132013+1)
= 20132012+1 / 20132013+1 = D
=> C < D nhé!
Ai k mk mk k lại!!
Mình sẽ ko làm nữa vì bài của các bạn kia đúng rùi
nhưng mong các bạn !!!
Thực hiện so sánh: A = 2013^2012+1/2013^2013+1
với 2013^2013 +1/ 2013^2014 + 1
thực hiện so sánh:
A=20132012+1/20132013+1 với B=20132013+1/20132014+1
So sánh:
A=\(\frac{2013^{2012}-1}{2013^{2013}-1}\)và B=\(\frac{2013^{2011}+1}{2013^{2012}+1}\)
A=\(\frac{2012}{2013}+\frac{2013}{2014}\) và \(\frac{2012+2013}{2013+2014}\)
so sánh nha!
giúp mk với!!!!
ta thấy:
\(\frac{2012}{2013}+\frac{2013}{2014}>\frac{2012}{2014}+\frac{2013}{2014}=\frac{2012+2013}{2014}>\frac{2012+2013}{2013+2014}\)
So sánh
\(A=\frac{2014^{2013}+1}{2014^{2013}-13}\)\(B=\frac{2014^{2012}+8}{2014^{2012}-11}\)
\(\frac{2014^{2013}+1}{2014^{2013}-13}\)lớn hơn 1 là \(\frac{14}{2014^{2013}-13}\)
\(\frac{2014^{2012}+8}{2014^{2012}-11}\)lớn hơn 1 là \(\frac{19}{2014^{2012}-11}\)
\(\frac{14}{2014^{2013}-13}\)\(< \)\(\frac{19}{2014^{2012}-11}\)
\(\Rightarrow A< B\)
So sánh:
A = \(\frac{2011^{2012}+1}{2011^{2013}+1}\)với B = \(\frac{2011^{2013}+1}{2011^{2014}+1}\)