S = 1.2+2.3+3.4+....+38.39+39.40

S.3 = ( 1.2+2.3+3.4+...+38.39+39.40 ) . 3

S.3 = 1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...........+38.39.(40-37)+39.40.(41-38)

S.3 = 1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...........+38.39.40-37.38.39+39.40.41-38.39.40

S = \(\frac{39.40.41}{3}\)

S = 13.40.41

S = 21320

S=1.2+2.3+...+39.40

3S=1.2.3+2.3.3+...+39.40.3

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=\(\frac{39.40.41}{3}\)

=>S=21320

\(S=1.2+2.3+3.4+...+39.40\)

\(\Rightarrow3S=3\left(1.2+2.3+3.4+...+39.40\right)\)

\(\Rightarrow3S=3.1.2+3.2.3+3.3.4+...+3.39.40\)

\(\Rightarrow3S=\left(3-0\right).1.2+\left(4-1\right).2.3+\left(5-2\right).3.4+...+\left(41-38\right).39.40\)

\(\Rightarrow3S=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+39.40.41-38.39.40\)

\(\Rightarrow3S=39.40.41\)

\(\Rightarrow S=\frac{39.40.41}{3}=21320\)

21320

S = 1 x 2 +2x3 + 3x4+... + 38x39+39x40  

3S= 1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3

3S=1.2.(3-0)+2.3(4-1)+...+38.39(40-37)

3S=0.1.2-1.2.3+1.2.3-2.3.4+...+37.39.39-38.39.40

3S=38.39.40

S=19760

S = 1 x 2 +2x3 + 3x4+... + 38x39+39x40
3S= 1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3
3S=1.2.﴾3‐0﴿+2.3﴾4‐1﴿+...+38.39﴾40‐37﴿
3S=0.1.2‐1.2.3+1.2.3‐2.3.4+...+37.39.39‐38.39.40
3S=38.39.40
S=19760

S = 1x2 + 2x3 + 3x4 + ... + 38x39 + 39x40

3S = 1x2x3 + 2x3x3 + 3x4x3 + ... + 38x39x3 + 39x40x3

3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 38x39x(40-37) + 39x40x(41-38)

3S = 1x2x3 + 2x3x4 -1x2x3 + 3x4x5-2x3x4 + ... + 38x39x40-37x38x39 + 39x40x41-38x39x40

S = 39x40x41 : 3

S = 21320

Đặt A = 1.2 + 2.3 + 3.4 + .... + 39.40

3A = 3( 1.2 + 2.3 + 3.4 + .... + 39.40 )

= 1.2.3 + 2.3.3 + 3.4.3 + .... + 39.40.3

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 39.40(41 - 38)

= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 39.40.41 - 38.39.40

= 39.40.41

\(\Rightarrow A=\frac{39.40.41}{3}=21320\)

s=2-1+3-2+...+39-38+40-39

  =40-1

 = 39

thank you

\(S=1.2+2.3+..........+39.40\)

\(3S=1.2.3+2.3.3+...........+39.40.3\)

\(3S=\left(3-0\right).1.2+\left(4-1\right).2.3.+......+\left(41-38\right).39.40.\)

\(3S=1.2.3-0.1.2+2.3.4-1.2.3+......+39.40.41-38.39.40\)

\(3S=0+39.40.41\)

\(3S=63960\)

   \(S=63960:3=21320\)