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a, 5M = 5+1+1/5+1/5^2+.....+1/5^2011
4M=5M-M=(5+1+1/5+1/5^2+.....+1/5^2011)-(1+1/5+1/5^2+.....+1/5^2012)
= 5-1/5^2012
=> M = (5 - 1/5^2012)/4
Tk mk nha
A=1+20121+20122+....+201272⇒2012A=2012+20122+....+201273⇒2011A=201273−1⇒A=201273−12011
=> A<B
M = 2012 + 20122 + 20123 + ... + 20122010
M = (2012 + 20122) + (20123 + 20124) + ... + (20122009 + 20122010)
M = 2012(1 + 2012) + 20123( 1 +2012) + ... + 20122009(1 + 2012)
M = 2012 . 2013 + 20123. 2013 + ... + 20122009 . 2013
M = 2013(2012 + 20123 + ... + 20122009)
=> M chia hết cho 2013 (đpcm)
m=2012+20122+20123+............+20122010
m=(2012+20122)+(20123+20124)+..........+(20122009+20122010)
m=(2012+2012.2012)+(20123+20123.2012)+...........+(20122009+20122009.2012)
m=2012.(2012+1)+20123.(2012+1)+............+20122009.(2012+1)
m=2012.2013+20123.2013+...........+20122009.2013
m=(2012+20123+...........+20122009).2013 chia hết cho 2013
=>đpcm
M = 2012 + 20122 + ... + 20122010
= ( 2012 + 20122 ) + ... + ( 20122009 + 20122010 )
= 2012( 1 + 2012 ) + ... + 20122009( 1 + 2012 )
= 2012.2013 + ... + 20122009.2013
= 2013( 2012 + ... + 20122009 ) chia hết cho 2013
hay M chia hết cho 2013 ( đpcm )
\(M=2012+2012^2+2012^3+...+2012^{2010}\)
\(M=\left(2012+2012^2\right)+\left(2012^3+2012^4\right)+...+\left(2012^{2009}+2012^{2010}\right)\)
\(M=2012\left(1+2012\right)+2012^3\left(1+2012\right)+...+2012^{2009}\left(1+2012\right)\)
\(M=2012.2013+2012^3.2013+...+2012^{2009}.2013\)
\(M=2013\left(2012+2012^3+...+2012^{2009}\right)⋮2013\) (đpcm)