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\(\left(7^{2014}:7^{2012}\right):7^{2012}\)
\(=7^2:7^{2012}\)
\(=\frac{7}{7^{2011}}\)
= (72014:72012):(72014:72012)
= 72 : 72
= 71 = 1
Hc tốt
#Mimi#


\(\frac{7^{2014}+7^{2012}}{7^{2012}}=\frac{7^{2012}\left(7^2+1\right)}{7^{2012}}=7^2+1=50\)

\(\left(7^{2014}+7^{2013}\right):7^{2012}\)
\(=7^{2014}:7^{2012}+7^{2013}:7^{2012}\)
\(=7^2-7\)
\(=49-7=42\)

\(TA-CO':\)
\(A=\frac{4+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}{7+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}\)
\(A=\frac{4\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}{7\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}\)
\(A=\frac{4}{7}\)
\(B=\frac{1+2+...+2^{2013}}{2^{2015}-2}\)
ĐẶT \(C=1+2+...+2^{2013}\)
\(\Rightarrow2C=2+2^2+...+2^{2014}\)
\(\Rightarrow2C-C=\left(2+2^2+...+2^{2014}\right)-\left(1+2+...+2^{2013}\right)\)
\(\Rightarrow C=2^{2014}-2\)
\(\Rightarrow B=\frac{2^{2014}-1}{2^{2015}-2}\)
\(B=\frac{2^{2014}-1}{2\left(2^{2014}-1\right)}\)
\(B=\frac{1}{2}\)
\(\Rightarrow A-B=\frac{3}{7}-\frac{1}{2}=\frac{6}{14}-\frac{7}{14}\)
\(A-B=\frac{6-7}{14}=\frac{-1}{14}\)
VẬY, \(A-B=\frac{-1}{14}\)
(72014+72012):72012 =72014 : 72012 + 72012 : 72012 =72 + 1 =49 +1=50