Tính nhanh: 1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + 98.99.100.
Giải thích
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100).4
4A=1.2.3(4 ‒ 0)+2.3.4(5 ‒ 1)+3.4.5(6 ‒ 2)+4.5.6(7 ‒ 3)+...+98.99.100(101 ‒ 97)
4A=1.2.3.4+2.3.4.5 ‒ 1.2.3.4+3.4.5.6 ‒ 2.3.4.5+4.5.6.7 ‒ 3.4.5.6+...+98.99.100.101 ‒ 97.98.99.100
4A=1.2.3.4 ‒ 1.2.3.4+2.3.4.5 ‒ 2.3.4.5+3.4.5.6 ‒ 3.4.5.6+...+97.98.99.100 ‒ 97.98.99.100+98.99.100.101
4A=98.99.100.101
Suy ra A = 98.99.100.101 : 4 = 24 497 550.