
Phan Thanh Tinh 20/04/2017 at 18:11
For any natural number m and n,we have :
\(\left(1000m+n\right)\left(m+n\right)=999m⋮9\)
So 1000m + n and m + n have then same remainder when divided by 999.Now we have :
100 + 101 and 100101 have the same remainder when divided by 999.
So do
100101 + 102 and 100101102
100101102 + 103 and 100101102103
...
100101102103104105106107 + 108 and 100101102103104105106107108
100 divided by 999 with remainder 100
=> 100101 ; 100101102 ; 100101102103 ; ... ; 100101102103104105106107 ; 100101102103104105106107108 divided by 9 with remainder
100 + 101
100 + 101 + 102
101 + 102 + 103
...
101 + 102 + 103 + ... + 107
101 + 102 + 103 + ... + 107 + 108
So the answer is : 101 + 102 + 103 + ... + 107 + 108 = 936
Selected by MathYouLike 
List of answers
We found following questions in our database that might relate to your problem. In some case you could find the solution from them.