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11.2+12.3+13.4+14.5+...+12015.2016+12016.2017
=1−12+12−13+13−14+14−15+...+12015−12016+12016−12017
=1−12017=20162017
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 1.2 + 2.3 + 3.4 + ... +2015.2016
3A = 1.2.3 + 2.3.(4-1) + ... + 2015.2016.(2017-2014)
3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 2015.2016.2017 - 2014.2015.2016
3A = 2014.2015.2016
A = 2727117120
![](https://rs.olm.vn/images/avt/0.png?1311)
4A= 4.( 1.2.3+2.3.4+4.5.6+5.6.7+...+2014.2015.2016
4A= 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .4.5.6.4 + ....+ 2014.2015.2016.4
4A= 1.2.3.4 + 2.3.4.(5 - 1)+ 3.4.5.( 6-2)+.....+ 2014.2015.2016.(2017-2013)
4A= 1.2.3.4+ 2.3.4.5-1.2.3.4.+ 3.4.5.6-2.3.4.5+ .....+ 2014.2015.2016.2017-2013.2014.2015.2016
4A = 2013.2014.2015.2016
A = 4117265071920
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A= 1.2+2.3+3.4+...+2015.2016
3A=1.2.3+2.3.3+3.4.3+...+2015.2016.3
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2015.2016.(2017-2014)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2015.2016.2017-2014.2015.2016
3A=2015.2016.2017
3A=8193538080
A=8193538080:3
A=2731179360
3A = 1.2.3 + 2.3.3 + 3.4.3 + ..... + 2015.2016.3
=> 3A = 1.2.3 + 2.3.( 4 -1 ) + 3.4.( 5 - 2 ) + .... + 2015.2016.( 2017 - 2014 )
=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + .... + 2015.2016.2017 - 2014.2015.2016
=> 3A = 2015.2016.2017
=> A = \(\frac{2015.2016.2017}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1.2+2.3+3.4+...+2015.2016
=> 3A=1.2.3+2.3.3+3.4.3+...+2015.2016.3
=> 3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2015.2016.(2017-2014)
=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+ 2015.2016.2017-2014.2015.2016
=> 3A=2015.2016.2017
=> A=\(\frac{2015.2016.2017}{3}=2731179360\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=1.2+2.3+3.4+...+2015.2016\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+2015.2016.3\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+2015.2016.\left(2017-2014\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2015.2016.2017-2014.2015.2016\)
\(\Rightarrow3A=2015.2016.2017\)
\(\Rightarrow A=2015.2016.2017:3\)
\(\Rightarrow A=2015.672.2017\)
Vậy \(A=2015.672.2017\)
1 . 2 + 2 . 3 + 3 . 4 + ... + 2015 . 2016
3M = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ... + 2015 . 2016 . 3
3M = 1 . 2 ( 3 - 0 ) + 2 . 3 ( 4 - 1 ) + 3 . 4 ( 5 - 2 ) + ... + 2015 . 2016 ( 2017 - 2014 )
3M = ( 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4. 5 + ... + 2015 . 2016 . 2017 ) - ( 0 . 1 . 2 + 1 . 2 . 3 + 2 . 3 . 4 + ... + 2014 . 2015 . 2016 )
3M = 2015 . 2016 . 2017
M = \(\frac{2015.2016.2017}{3}\)
M = 2731179360
![](https://rs.olm.vn/images/avt/0.png?1311)
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+............+2015.2016.(2017-2014)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.............+2015.2016.2017-2014.2015.2016
3A=2015.2016.2017
A=2015.2016.2017:3
A=2015.672.2017