Question

Tính: S = 1 x 2 + 2 x 3 + 3 x 4 + .... + 39 x 40

Answer 1

S = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 39 x 40

3S = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + 4 x 5 x 3 + ... + 39 x 40 x 3

3S = 1x2x3 + 2x3x(4-1 ) + 3x4x(5-2 ) + 4x5x(6-3 ) + ... + 39x40x(41-38 )

3S = 1 x 2x3 + 2x3x4-1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 39x40x31 - 38x39x40

3S = 39x40x41

S = 39x40x41 : 3

S = 21320

Answer 2

S=1*2+ 2*3 + 3*4 +.....+ 39*40

S=  2  +  6+   12  + ....+ 1560

S=  2   + 0 + 4 + 2 +6 + 4 + 2+ ....... + 1554 + 4 +2

S=  2   + 0  +    6   +6  +     6    + ....... +1554 +      6

S=  2    + ( 0 + 6 + ..... +1554)+ ( 6 * ((1554-0):6+1))

S =  2    +          202020         +   1560

S = 203582