Discussion
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?
*This question is included in Nova Press: Set E - Number Theory, question #18
| (A) | S is always odd. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
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
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.
Nova Press
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.
Nova Press