Câu 1 :
So sánh:
A = \(\frac{-9}{10^{2013}}\)+\(\frac{-19}{10^{2014}}\)và B=\(\frac{-9}{10^{2014}}\)+\(\frac{-19}{10^{2013}}\)
1.so sánh
a. A=\(\frac{2005^{2005}+1}{2005^{2006}+1}\) và B=\(\frac{2005^{2004}+1}{2005^{2005}+1}\)
b. A=\(\frac{20^{10}+1}{20^{10}-1}\) và B=\(\frac{20^{10}-1}{20^{10}-3}\)
c. A=\(\frac{2009^{2009}+1}{2009^{2010}+1}\) và B=\(\frac{2009^{2010}+2}{2009^{2011}-2}\)
d. A=\(\frac{2013^{2014}+2014}{2013^{2014}-2014}\) và B=\(\frac{2013^{2014}-2014}{2013^{2014}-6042}\)
Hãy so sánh :
\(A=\frac{10^{2012}+1}{10^{2013}+1} \) và \(B=\frac{10^{2013}+1}{10^{2014}+1}\)
\(A=\frac{10^{2012}+1}{10^{2013}+1}\)
\(10A=\frac{10\cdot\left[10^{2012}+1\right]}{10^{2013}+1}=\frac{10^{2013}+10}{10^{2013}+1}=\frac{10^{2013}+1+9}{10^{2013}+1}=1+\frac{9}{10^{2013}+1}\)
\(B=\frac{10^{2013}+1}{10^{2014}+1}\)
\(10B=\frac{10\cdot\left[10^{2013}+1\right]}{10^{2014}+1}=\frac{10^{2014}+10}{10^{2014}+1}=\frac{10^{2014}+1+9}{10^{2014}+1}=1+\frac{9}{10^{2014}+1}\)
Mà \(1+\frac{9}{10^{2013}+1}>1+\frac{9}{10^{2014}+1}\)
Nên \(10A>10B\)
Hay \(A>B\)
Vậy : A > B
Cho A = \(\frac{10^{2012}-2}{10^{2013}-1}\); B = \(\frac{10^{2013}-2}{10^{2014}-1}\)
So sánh A và B
TA có :
A = \(\frac{10^{2012}-2}{10^{2013}-1}\)=> 10A = \(1-\frac{19}{10^{2013}-1}\)
B = \(\frac{10^{2013}-2}{10^{2014}-1}\)=> 10B = 1 - \(\frac{19}{10^{2014}-1}\)
Vì \(1-\frac{19}{10^{2013}-1}\)< 1 - \(\frac{19}{10^{2014}-1}\)hay 10A < 10B => A < B
Vậy A < B
Câu 5. (1,0 điểm)
Cho tổng A gồm 2014 số hạng: A = \(\frac{1}{19}+\frac{2}{19^2}+\frac{3}{19^3}+..........+\frac{2014}{19^{2014}}\)
Hãy so sánh A2013 và A2014.
So sánh :\(A=\frac{10^{2012}}{10^{2013}+1}vàB=\frac{10^{2013}}{10^{2014+1}}\)
So sánh A và B biết rằng:
A = \(\frac{10^{2013}+1}{10^{2014}+1}\); B = \(\frac{10^{2014}+1}{10^{2015}+1}\)
- Cần câu trả lời gấp
So Sánh
A=\(\frac{10^{2013}+1}{10^{2014}+1}\)
B=\(\frac{10^{2014}+1}{10^{2015}+1}\)
Vì \(\frac{10^{2014}+1}{10^{2015}+1}< 1\Rightarrow B=\frac{10^{2014}+1}{10^{2015}+1}< \frac{10^{2014}+1+9}{10^{2015}+1+9}\)
\(\Rightarrow B< \frac{10^{2014}+10}{10^{2015}+10}\)
\(\Rightarrow B< \frac{10\left(10^{2013}+1\right)}{10\left(10^{2014}+1\right)}\)
\(\Rightarrow B< \frac{10^{2013}+1}{10^{2014}+1}\)
\(\Rightarrow B< A\)
Vậy A > B
Thực hiên so sánh A=\(\frac{20132013}{20142014}\)với B=\(\frac{131313}{141414}\)
b)C=20139+201310 với D = 201410
So sánh không qua quy đồng:
\(A=\frac{-7}{10^{2013}}+\frac{-15}{10^{2014}}\)
\(A=\frac{-15}{10^{2013}}+\frac{-7}{10^{2014}}\)
\(\frac{-7}{10^{2013}}\)+\(\frac{-15}{10^{2014}}\) > \(\frac{-15}{10^{2013}}\)+\(\frac{-7}{10^{2014}}\)