Tinh S =1.2+2.3+4.3+.........+39.40
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S=1.2+2.3+3.4+...+39.40
3S=1.2.3+2.3.3+3.4.3+...+39.40.3
3S=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+39.40.(41-38)
3S=1.2.3+1.2.0+2.3.4+2.3.1+3.4.5+3.4.2+...+39.40.41+39.40.38
3S=1.2.0+39.40.41= 63960
S=63960 :3= 21320
Vậy S= 21320
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=1\cdot2+2\cdot3+3\cdot4+....+39\cdot40\)
\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+39\cdot40\cdot\left(41-38\right)\)
\(=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+.....+39\cdot40\cdot41-38\cdot39\cdot40=39\cdot40\cdot41=63960\)
S=21320
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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: S = 1.2+2.3+3.4+...+39.40
=> 3S = 1.2.(3 - 0) + 2.3.(4 - 1) + ..... + 39.40.(41 - 38)
=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 39.40.41
=> 3S = 39.40.41
=> S = 39.40.41/3
=> S = 21320
![](https://rs.olm.vn/images/avt/0.png?1311)
3S=1.2.3+2.3.(4-1)+...+39.40.(41-38)
=1.2.3+2.3.4+...+39.40.41-1.2.3-...38.39.40(triệt tiêu đi)
=39.40.41
vậy S=\(\frac{39.40.41}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=1.2+2.3+...+39.40
3S=1.2.(3 - 0)+2.3.(4 - 1)+...+39.40.(41 - 38)
3S=1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 39.40.41 - 38.39.40
3S=39.40.41
S=13.40.41
S=21320
=39 . 40 . 41 / 3
3S=1.2.3+2.3.3+...+39.40.3
3S=1.2.3+2.3.(4-1)+...+39.40.(41-38)
3S=1.2.3-1.2.3+2.3.4-...-38.39.40+39.40.41
3S=39.40.41
S=13.40.41
S=21320