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14 Jun 2010, 00:18
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I'm not sure where to post this since I am not looking for an answer to a specific problem, rather confirmation on a potential number property. If true, I'd use it for data sufficienty so I'm posting here.
I am familiar with the following property: The sum of n consecutive integers is divisible by n if n is odd, but it is not divisible by n if n is even.
This makes logical sense. However, I was curious about scenarios in which n=even, so started messing around with numbers. After experimenting with several sets, it appears that if n=even, the sum of n consecutive integers is divisible by n/2. I've tested this with many number sets and it appears to be true. Can anyone confirm?
I am familiar with the following property: The sum of n consecutive integers is divisible by n if n is odd, but it is not divisible by n if n is even.
This makes logical sense. However, I was curious about scenarios in which n=even, so started messing around with numbers. After experimenting with several sets, it appears that if n=even, the sum of n consecutive integers is divisible by n/2. I've tested this with many number sets and it appears to be true. Can anyone confirm?
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14 Jun 2010, 03:36
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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.
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.
15 Jun 2010, 01:21
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vinay,
I would like to post a correction here regarding your post if you dont mind. You have told that sum of n consecutive integers is n(n+1)/2 which is only correct if your first integer is 1. If you start your series with any other number than 1, this formula is no more vaild.
I would like to post a correction here regarding your post if you dont mind. You have told that sum of n consecutive integers is n(n+1)/2 which is only correct if your first integer is 1. If you start your series with any other number than 1, this formula is no more vaild.
