Question

1*2+2*3+3*4+..98*99+99*100

Answer 1

Đặt A = 1 x  2 + 2 x 3 + .........+ 99 x 100

3A = 1 x 2 x 3 + 2 x 3 x 3 +.........+99 x 100 x 3

3A = 1 x 2 x (3-0) + 2 x 3 x (4-1) +........ + 99 x 100 x (101 - 98)

3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 +............ + 99 x 100 x 101 - 98 x 99 x 100

3A = (1x2x3 - 1x2x3) + (2x3x4-2x3x4) +.............+ (98x99x100 - 98 x99x100) + 99 x 100 x 101

3A = 99 x 100 x 101 = 999900

A = 999900 : 3 = 333300