Question

1x2 + 2x3 +3x4 +.........+99x100

lâu ngày k làm quên gùichỉ mìn nha

Answer 1

Đặt A=1.2+2.3+3.4+...+99.100

=>3A=3(1.2+2.3+3.4+...+99.100)

=>3A=1.2.3+2.3.3+3.4.3+...+99.100.3

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

=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100

3A=(1.2.3-1.2.3)+(2.3.4-2.3.4)+...+(98.99.100-98.99.100)+99.100.101

3A=0+0+...+0+99.100.101

3A=99.100.101

A=99.100.101:3

A=333300

Vậy A=333300