Question

Tính: A=1x2x3+2x3x4+…+100x101x102

Answer 1

A = 1x2x3 + 2x3x4 +…+ 100x101x102
Nhân A với 4 ta có :
A x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +…+100x101x102x4
A x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 100x101x102x(103 - 99)
A x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... + 100x101x102x103 - 99x100x1001x102
Sau khi cộng - trừ giản ước ta có : A x 4 = 100x101x102x103
A = 100 x101x102x103 : 4 = 26527650