Question

[Nguyễn Huyền Linh]

Tính: S= 1x2+2x3+3x4+... +38x39+39x40

Answer 1

[Isolde Moria]

Ta có

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

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

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

\(\Rightarrow S=\frac{38.39.40}{3}\)

\(\Rightarrow S=21320\)

Answer 2

[Nguyễn Hải Dương]

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