Số học 6 1 số dạng

Câu 1 :
a) 1.2.3+2.3.4+3.4.5+...+97.98.99
Gọi dãy số trên là A , ta có :
4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 +... +97.98.99.4
4A = 1.2.3(4-0) +2.3.4(5-1) + ... + 97.98.99(100-96)
4A = 1.2.3.4 - 1.2.3.0 + 2.3.4.5 - 2.3.4.1 + ... + 97.98.99.100-97.98.99.96
4A = 97.98.99.100
A = 97.98.99.10 : 4
b) 2.2 + 4.4 + 6.6 + 8.8 +...+ 100 .100
2A = 2.2.2 + 4.4.2 + 6.6.2 + ... + 100 .100.2
2A = 2.(3+1) + 4.(3+5) + ....+ 100(99+101)
2A = 2.3 + 1.2 + 4.3 + 4.5 + ....+ 100.99 + 100.101
6A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 100.99.3 + 100.101.3
6A = 1.2(3-0) + 2.3(4-1) + ... + 100.99(101-98) + 100.101(102-99)
6A = 1.2.3 - 1.2.0 + 2.3.4 - 1.2.3 + .... + 99.100.101 - 98.99.100 + 100.101.102 - 99.100.101
6A = 100.101.102
A = 100.101.102 : 6
Câu2 :
a) 1.3.5.....39
21.22.....40
= (1.3.5...39)(2.4.6...40)
(21.22....40)(1.2...20). 220
= 1.2.3.4........40
(1.2.3....40).2 mũ 20
= 1
220