Question

  Tính tích     S =  1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13

Answer 1

S =  1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3

Ta lấy K = 1x2x3 +2x3x4  + 3x4x5 + ……   + 11x12x13 + 12x13x14
 -     3S  = 1x2x3 + 2x3x3 + 3x4x3+ ………  + 11x12x3  + 12x13x3
            ------------------------------------------------------------------------------------
 K – 3S =     0     + 2x3x1  + 3x4x2 + …… .. + 11x12x10 + 12x13x11

K – 3S =   K – 12x13x14
Từ đó suy ra:   3S = 12x13x14
S = 4x13x14 = 728  

Answer 2

S=1x2 + 2x3 + 3x4 + ... + 11x12 + 12x13

3S=1x2x3 + 2x3x3 + 3x4x3 + ... + 11x12x13 

    =1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 11x12x(13-10)

    =1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 11x12x13 - 10x11x12

    =\(\frac{10x11x12}{3}\) = 1320 

Answer 3

Lộn đề rùi Đây mới là bài giải đúng nè S=1x2 + 2x3 + 3x4 + ... + 11x12 + 12x133S= 1x2x3 + 2x3x3 + 3x4x3 + ... + 11x12x13 + 12x13x13    = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 11x12x(13-10) + 12x13x(14-11)    = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 11x12x13 - 10x11x12 + 12x13x14 - 11x12x13    = (12x13x14) : 3          = 728