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Thread: Triangular Numbers.

  1. #1
    Expert Member
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    Jun 2006
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    Triangular Numbers.

    The triangular numbers are the numbers 1,3,6,10,15,21,28,36 and so on.

    How many of the first 250 triangular numbers are divisible by 5?


  2. #2
    Junior Member
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    Nov 2006
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    6

    Re: Triangular Numbers.

    For every 5 triangular numbers, 2 are divisible by 5
    So in the first 250 triangular numbers 250/5 * 2 = 100 numbers will be divisible by 5


  3. #3
    Expert Member
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    Jun 2006
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    Re: Triangular Numbers.

    Yeah. Hari is right.

    The statment 'For every 5 triangular numbers, 2 are divisible by 5' make by Hari is the key here. Let me justify that statment

    It is obvious that an nth triangular number is the sum of first n natural numbers which is equal to n(n-1)/2). So if a triangular number is divisible by 5 then either n or n-1 is divisible by 5.

    There are two such numbers in every 5 triangular numbers which have either n or n-1 divisible by 5.


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