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Number sequence

  1. Feb 19, 2014 #1
    For a system I am studying the following sequence (which I would assume is quite common) came up:

    n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 .... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1).
    Is there a closed form expression f(k) for this sequence, i.e. f(1)=n1, f(2)=n2, f(3)=n3 etc.

    edit: So basically I have a sequence with I think what is called a recurence relation equal to:

    x_n+1 = x_n+n

    Can I find a closed form for this?
     
  2. jcsd
  3. Feb 19, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    Hint:
    [tex]
    \sum_{k=1}^n k - \sum_{k=1}^{n-1} k = n
    [/tex]

    The sum can be expressed in closed form as a standard result.
     
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