A=1/2 +1/2mu 2+...+1/2 mu 15
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28 tháng 7 2018
A= \(2^0+2^1+2^2+...+2^{50}\)
\(\Rightarrow\)2A =2(\(2^0+2^1+2^2+...+2^{50}\))
\(\Rightarrow\)2A= \(2+2^2+2^3+2^4+...+2^{51}\)
\(\Rightarrow\)2A-A= (\(2+2^2+2^3+2^4+...+2^{51}\))-(\(2+2^2+2^3+2^4+...+2^{50}\))
\(\Rightarrow\)A= \(2^{51}-1\)
T
Cm 1/2 mu 2 - 1/ 2mu 4 + 1/ 2 mu 6-...-1/2mu 4n -2 -1/2 mu 4n + ...+ 1/ 2 mu 2014 - 1/ 2 mu 2016<0,2
0
T
Cm 1/2 mu 2 - 1/ 2mu 4 + 1/ 2 mu 6-...-1/2mu 4n -2 -1/2 mu 4n + ...+ 1/ 2 mu 2014 - 1/ 2 mu 2016<0,2
3
9 tháng 9 2020
\(A=\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-...+\frac{1}{2^{2014}}-\frac{1}{2^{2016}}\)
\(\Rightarrow2^2A=1-\frac{1}{2^2}+\frac{1}{2^4}-\frac{1}{2^6}+\frac{1}{2^8}-...+\frac{1}{2^{2012}}-\frac{1}{2^{2014}}\)
\(\Rightarrow2^2A+A=1+\left(\frac{1}{2^2}-\frac{1}{2^2}\right)+\left(\frac{1}{2^4}-\frac{1}{2^4}\right)+...+\left(\frac{1}{2^{2014}}-\frac{1}{2^{2014}}\right)-\frac{1}{2^{2016}}\)
\(\Rightarrow5A=1-\frac{1}{2^{2016}}< 1\Rightarrow A< \frac{1}{5}=0,2\)
LM
0
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{15}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{14}}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{14}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{15}}\right)\)
\(A=1-\frac{1}{2^{15}}\)\
\(A=1-\frac{1}{32768}\)
\(A=\frac{32767}{32768}\)