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If n > 2, then the sum, S, of the integers from 1 through n can be calculated ... ...

If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
(A) S is always odd.
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Press: Set E - Number Theory

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Replies to This Thread: 1 | ----
If n > 2, then the sum, S, of the integers from 1 through n can be calculated ... ... 
Posted: 08/05/2013 23:46
Agree, I have an enquiry why the B answer is not right either? The multiplication of consecutive number which is >2 is always even. For instance, n=3(odd), n+1=4 (even) so we got 12/2=6 and if n=4(even), n+1=5(odd) so we also got 20/2=10 (even) because odd*even=even/2=even the remainder is 0. Thank you
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Posted: 08/06/2013 15:08
Hi Oktarico,

For n = 5, the expression is odd:

n(n + 1)/2 = 5(5 + 1)/2 = 5(6)/2 = 5(3) =15.

Sometimes when you divide an even number by 2, the result is even, but sometimes it is odd.

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