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A=2+22+23+...+22013
A=(2+22+23)+...+(22011+22012+22013)
A=2(1+2+22)+...+22011(1+2+22)
A=2.7+...+22011.7
A=7(2+...+22011) chia hết cho 7
=>A chia hết cho 7
tick tớ nha
\(A=\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{4}\right)^2+...+\left(\dfrac{1}{2013}\right)^2\)
\(A=\left(\dfrac{1}{2+3+4+...+2013}\right)^2\)
\(A=\left(\dfrac{1}{\left(2013-2\right)+1}\right)^2\)
\(A=\left(\dfrac{1}{2012}\right)^2\)
\(A=\dfrac{1}{2012\cdot2012}\)
\(\Rightarrow A=\dfrac{1}{2012}< \dfrac{3}{4}\)
a) 2011 . 2013 = 2011 . ( 2012 + 1 ) = 2011 . 2012 + 2011
20122 = 2012 . 2012 = ( 2011 + 1 ) . 2012 = 2011 . 2012 + 2012
Vì 2011 . 2012 + 2011 < 2011 . 2012 + 2012 nên 2011 . 2013 < 20122
\(\left(x+1\right)^3=27\)
\(\left(x+1\right)^3=3^3\)
\(\Rightarrow x+1=3\)
\(x=2\)
\(\left(x+1\right)^3=27\)
\(< =>\left(x+1\right)^3=3.3.3=3^3\)
\(< =>x+1=3< =>x=3-1=2\)
\(\left(2x+3\right)^3=9.81\)
\(< =>\left(2x+3\right)^3=9.9.9\)
\(< =>\left(2x+3\right)^3=9^3\)
\(< =>2x+3=9< =>2x=6\)
\(< =>x=\frac{6}{2}=3\)
A=2014/2013 B=2013/2012
A=1-2014/2013 B=1-2013/2012
A=-1/2013 B=-1/2012
=>-1/2013 > -1/2012
VẬY A=2014/2013>B=2013/2012
\(M=1+2+2^2+...+2^{2013}\)
\(\Rightarrow2M=2+2^2+2^3+...+2^{2014}\)
\(\Rightarrow2M-M=2^{2014}-1\)
\(\Leftrightarrow M=2^{2014}-1\)
1/2 mũ 2 + 1/4 mũ 2+ 1/6 mũ 2 +....+1/1000 mũ 2