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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1.2 + 2.3 + 3.4 + ... + 2013.2014
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2013.2014.3
Mà :
1.2.3 = 1.2.3
2.3.3 = 2.3.4 - 2.3.1
3.4.3 = 3.4.5 - 3.4.2
2012.2013.3 = 2012.2013.2014 - 2012.2013.2011
2013.2014.3 = 2013.2014.2015 - 2013.2014.2012
Cộng tất cả, vế theo vế ---> 3S = 2013.2014.2015
---> A = 2013.2014.2015 / 3 = 2723058910.
của bạn đây
![](https://rs.olm.vn/images/avt/0.png?1311)
Tính tổng : A=1.2+2.3+3.4+..+19.20
3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 19.20.21
3A = 19.20.21
A = \(\frac{19.20.21}{3}=3990\)
Tính tổng : A=1.2+2.3+3.4+..+19.20
3a=1.2.3-1.2.3.+2.3.4-2.3.4+......+19.20.21
3a=19.20.21
a=19.20.21:3=3990
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
3S=1.2.3+2.3.3+3.4.3+...+49.50.3
=1.2.3+2.3.(4-1)+3.4.(5-2)+...+48.49.(50-47)+49.50.(51-48)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+48.49.50-47.48.49+49.50.51-48.49.50
=(1.2.3-1.2.3)+(2.3.4-2.3.4)+...(47.48.49-47.48.49)-(48.49.50-48.49.50)+49.50.51
=0+0+...+0+0+49.50.51
=49.50.51
\(S=\frac{\left(49.50.51\right)}{3}\)
=41650
Đáp số:41650
3A=1.2.3+2.3.3+..............+150.151.3
=1.2.3+2.3.(4-1)................+150.151.(152-149)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....................+150.151.152-149.150.151
=150.151.152
=>A=\(\frac{150.151.152}{3}\)
A=1147600
thấy ổn thì t nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1.2 + 2.3 + 3.4 + ... + 2013.2014
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2013.2014.3
Mà :
1.2.3 = 1.2.3
2.3.3 = 2.3.4 - 2.3.1
3.4.3 = 3.4.5 - 3.4.2
2012.2013.3 = 2012.2013.2014 - 2012.2013.2011
2013.2014.3 = 2013.2014.2015 - 2013.2014.2012
Cộng tất cả, vế theo vế ---> 3S = 2013.2014.2015
---> A = 2013.2014.2015 / 3 = 2723058910
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
![](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
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)
![](https://rs.olm.vn/images/avt/0.png?1311)
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 49.50.3
3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 49.50.51 - 48.49.50
3A = 49.50.51
A = 41650
\(A=1.2+2.3+3.4+....+49.50\)
\(3A=1.2.3+2.3.3+3.4.3+....+49.50.3\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+....+49.50.\left(51-48\right)\)
\(3A=1.2.3+2.3.4+3.4.5+....+49.50.51\)
\(3A=49.50.51=124950\)
\(\Rightarrow A=\frac{124950}{3}=41650\)