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The sum of N consecutive integers: S=(n+n+N-1)*N/2=n*N+N*(N-1)/2 S/N=n+(N-1)/2 If N is odd, then S would be a multiple of N. If N is even, then S would not be a multiple of N.

i don't understand this.....

It simply means that if you are adding N consecutive integers then their sum S will be a multiple of N if N=odd

i.e for example

let suppose a series of 1,2,3,4,5 total integers =5 (N=5)

sum of integers=15 (1+2+3+4+5)

then 15 is a multiple of 5 i.e N

this is the only for N= odd not for N= even
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