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Math Help - Consecutive numbers

  1. #1
    xjx
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    Consecutive numbers

    can anyone shed any light on this problem. i don't know where to start!

    'Many numbers can be expressed as the sum of two or more consecutive integars.

    For example:
    15=7+8
    10=1+2+3+4

    Can you say which numbers can be expressed this way and which numbers cannot be?
    Can you prove your statements?'

    So I understand that I have to go through the numbers and work out which are and aren't (e.g 1+2=3 so 3 works, then the next that works would be 2+3=5).

    Can anyone see any particular ways I should go about doing this? Also what does it mean by can you prove your statements?

    Any suggestions?
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  2. #2
    MHF Contributor Quick's Avatar
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    What level of math are you in? (I don't want to give too confusing an answer)
    Last edited by Quick; September 24th 2006 at 10:29 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by xjx View Post
    can anyone shed any light on this problem. i don't know where to start!

    'Many numbers can be expressed as the sum of two or more consecutive integars.

    For example:
    15=7+8
    10=1+2+3+4

    Can you say which numbers can be expressed this way and which numbers cannot be?
    Can you prove your statements?'

    So I understand that I have to go through the numbers and work out which are and aren't (e.g 1+2=3 so 3 works, then the next that works would be 2+3=5).

    Can anyone see any particular ways I should go about doing this? Also what does it mean by can you prove your statements?

    Any suggestions?
    The sum of n terms of an arithmetic progressiosn with first term a1
    and common difference d is:

    Sn=a1 + a2 + ... + an=n.a1+n(n-1)d/2.

    So the sum of consecutive integers will be such a sum with a common
    difference d=1, so

    Sn=n.a1+n(n-1)/2,

    which is the (n-1)th triangular number plus some multiple of n.

    RonL
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  4. #4
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    I answered this question a long time ago, those numbers that are exponents of two cannot be expressed as a sum of consecutives.
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