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What is the formal proof that a sequence diverges

  1. Dec 2, 2008 #1
    i got (n^2+1)/n
    when n->infinity the limit is infinity.
    what is the formal proof that a sequence diverges ?
  2. jcsd
  3. Dec 2, 2008 #2
    I don't know the formal proof off by heart, but you could use L'Hopital's rule to see that it diverges(?).
  4. Dec 2, 2008 #3


    Staff: Mentor

    Show that for any (large, positive) number M, there exists another number N for which, if n >= N, then a_n > M.

    So someone gives you a number M.
    You find another number N so that a_N+1, a_N+2, a_N+3, ... all are larger than M.

    For your sequence, solve (n^2 + 1)/n > M for n. From that, choose a number N.

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