dãy tính có quy luật

Question

1.2.3+2.3.4+3.4.5+...18.19.20

Answer 1

Ta có :
1.2.3 + 2.3.4 + 3.4.5 + 5.6.7 + ... + 17.18.19 + 18.19.20
= 3.(2 + 2.4 + 4.5 + 5.2.7 + ... + 17.6.19 + 6.19.20)
= 3.[2 + 8 + 20 + 70 + ... + 6.19.(17 + 20)]
= 3.[100 + 112 + 168 + 240 + 3.10.11 + 10.11.4 + 11.4.13 + 4.13.14 + ... + 6.19.(17 + 20)]
= 3.[100 + 520 + 10.11.(3 + 4) + 4.13.(11 + 14) + ... + 6.19.(17 + 20)]
= 3.(620 + 110.7 + 52.25 + ... + 114.37)
= 3.(620 + 770 + 1300 + ... + 4218)
= 3.(620 + 770 + 1300 + 2030 + 1360 + 4218)
= 3.10 298
= 30 894