Question

tính tổng S=1x2+2x3+.......+99x100 

Answer 1

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

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

3S = 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

3S = (1 x 2 x 3 - 1 x 2 x 3) + (2 x 3 x4 - 2 x 3 x4) +....... + (98 x 99 x 100 - 98x 99 x 100) + 99 x 100 x 101

3S = 99 x 100 x 101 = 999900

S = 999900 : 3 = 333300 

Vậy S = 333300