\(S=1x2+2x3+3x4+...+39x40\)
\(\Rightarrow3S=1x2\left(3-0\right)2x3\left(4-1\right)+...+39x40\left(41-38\right)\)
\(\Rightarrow3S=1x2x3-0x1x2+2x3x4-1x2x3+...+39x40x41-38x39x40\)
\(\Rightarrow S=\frac{38x39x40}{3}\)
\(\Rightarrow S=21320\)
\(S=1.2+2.3+3.4+...+38.39+39.40\)
\(3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+38.39.\left(40-37\right)+39.40.\left(41-38\right)\)
\(3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+38.39.40-37.38.39+39.40.41-38.39.40\)
\(3S=39.40.41\)
\(S=\frac{63960}{3}=21320\)
. là nhân
S = 1x2+2x3+3x4+...+39x40
3S = 1x2x3 + 2x3x3 + 3x4x3 + ... + 39x40x3
3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 39x40x(41-38)
3S = 1x2x3 + 2x3x4-1x2x3 + 3x4x5 - 2x3x4 + ... + 39x40x41 - 38x39x40
3S = 39x40x41
S = 39x40x41 : 3
S = 21320