Question

1*2+2*3+3*4+...+99*100=?

Answer 1

Đặt S = 1.2 + 2.3 + 3.4 +...+ 99.100

3S = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101 - 98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +...+ 99.100.101 - 98.99.100

3S = 99.100.101

3S = 999900

S = 333300

Answer 2

=>3S+1.2.3+2.3.3+...+99.100.3

=>123+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

=>1.2.3+2.3.4-1.2.3+3.4.5+(-2).3.4+...+99.100.101-98.100.101

=>3S=99.100.101

3S=999900

S=999900:3

S=333300