Yes, your assumption must be true. Because, sum of n consecutive integers is n(n+1)/2. Now, if you take N as odd, sum would always be divisible by n. Because, sum would be n*some integer (since n+1 would be even, if n is odd and it would definitely be divisible by 2).

Similarly, if n is even, n(n+1)/2 would covert to n/2 as integer as n is even and n+1 which will be an odd number.

Hence, by algebraically, you can come to this conclusion. Please let me know if you have any queries on the explanation.

_________________

-------------------------------------

Please give kudos, if my post is helpful.

For English Grammar tips, consider visiting http://www.grammar-quizzes.com/index.html.