Question

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

Answer 1

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

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

3S = 1.2.3+2.3.3+3.3.4+......+3.38.39+3.39.40

3S = 1.2.3+2.3.(4-1)+3.4.(5-2)+.....+38.39.(40-37)+39.40.(41-38)

3S = 1.2.3+2.3.4-2.3.1+3.4.5-3.4.2+......+38.39.40-38.39.37+39.40.41-39.40.38

3S = (1.2.3-2.3.1)+(2.3.4-3.4.2)+.....+(38.39.40-39.40.38)+39.40.41

3S = 39.40.41

S = (39.40.41) :3

S = (39:3).40.41

S = 13.40.41=21320

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Answer 2

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

\(\Rightarrow3S\) = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + .... + 38x39x(40-37) + 39x40x(41-38)

\(\Rightarrow3S=\) 1x2x3 - 1x2x3 + 2x3x4 - 2x3x4 +3x4x5 +.... + 38x39x40 - 37x38x39+ 39x40x41-38x39x40

\(\Rightarrow3S=\)39x40x41 = 63 960

\(\Rightarrow S\) = 63960 : 3 = 21320

Answer 3

Ta có: 3S = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 38 . 39 . (40 - 37) + 39 . 40 . (41 - 38)

3S = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 38 . 39 . 40 - 37 . 38 . 39 + 39 . 40 . 31 - 38 . 39 . 40

3S = 39 . 40 . 41

S = 13 . 40 . 41 = 21320

Answer 4

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

3S= 1x2x3+2x3x3+3x4x3+...+38.39.3+ 39x40x3

3S= 1x2x(3-1)+2x3x(4-2)+4x3x(5-3)+...+38x39x(40-37)+39x40x(41-38)

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

3S= 39x40x41=63960

⇒S= 63960:3= 21320

Vậy S=21320