Question

Tính : \(S\)=\(\text{1x2+2x3+3x4+.......+49x50}\)

Answer 1

S = 1 . 2 + 2 . 3 + 3 . 4 + ... + 49 . 50

=> 3S = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ... + 49 . 50 . 3

=> 3S = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 49 . 50 . (51 - 48)

=> 3S = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 49 . 50 . 51 - 48 . 49 . 50

=> 3S = 49 . 50 . 51

=> S = (49 . 50 . 51)/3

=> S = 124950/3

=> S = 41650

Vậy S = 41650.