Câu hỏi của Hatake Kakashi

Question

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

Nguyễn Ngọc Quý · Accepted Answer

Đặt S = 1 x 2 + 2 x 3 + ......... + 99 x100

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

3S = 99 x 100 x 101

S = 99 x 100 x 101 : 3 = 333300

Câu trả lời:

Đặt S = 1 x 2 + 2 x 3 + ......... + 99 x100

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

3S = 99 x 100 x 101

S = 99 x 100 x 101 : 3 = 333300