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Proving a formula for the number of intervals contained in [1,n]

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove a simple formula for the number of closed intervals with integer endpoints contained in the interval [1,n] (including one point intervals), where n is a natural number.

    3. The attempt at a solution
    I know that the formula ends up being the sum of i from i=1 to i=n (this makes sense just from inspection) but I have no idea how to actually go about proving the claim.
  2. jcsd
  3. Feb 24, 2010 #2


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    Welcome to PF!

    Hi morbius27! Welcome to PF! :wink:

    Try it for n = 4 first …

    write out a list of all the closed intervals …

    what do you get? when you count them, can you see a pattern? :smile:
  4. Feb 24, 2010 #3
    if you know the solution but want to prove it, use induction
  5. Feb 24, 2010 #4
    Re: Welcome to PF!

    Thanks Tiny Tim! I got the solution after doing what you said and got the pattern; it worked beautifully after that ;)
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