Đặt M = 1 . 2 + 2 . 3 + ... + 99 . 100
3M = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 3 + ... + 99 . 100 . 3
3M = 1 . 2 . ( 3 - 0 ) + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) ... . 99 . 100 . ( 101 - 98 )
3M = ( 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 +... + 99 . 100 . 101 ) - ( 0 . 1 . 2 + 1 . 2 . 3 + 2 . 3 . 4 +.......+ 98 . 99 . 100 )
3M = 99 . 100 . 101 - 0 . 1 . 2
3M = 999900 - 0 = 999900
M = 999900 : 3
M = 333300
ban oi giai cach khac cach nay minh roi
Đặt A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100
3 . A = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ... + 99 . 100 . 3
3 . A = 1 . 2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + ... + 99 . 100 . ( 101 - 98 )
3 . A = ( 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + ... + 99 . 100 . 101 ) - ( 0 . 1 . 2 + 1 . 2 . 3 + 2 . 3 . 4 + ... + 98 . 99 . 100 )
3 . A = 99 . 100 . 101 - 0 . 1 . 2
3 . A = 999900 - 0
3 . A = 999900
A = 999900 : 3
A = 333300
Vậy 1 . 2 + 2 . 3 + 3 . 4 + ... + 99 .100 = 333300