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Show sequence converges?

  1. Sep 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the sequence P_n = [(n+1)/n, [(-1)^n]/n] converges.

    2. Relevant equations

    A sequence p_n converges to a point p if and only if every neighborhood about p contains all the terms p_n for sufficiently large indices n; to any neighborhood U about p, there corresponds an index N such that p_n exists in U whenever n > or = N.

    3. The attempt at a solution

    The sequence converges to the point p = (1 0). Let U be the open ball around p with radius r>0. Need to show that |p_n - p|< r for all n > or = N i.e. ....

    |((n+1)/n, ((-1)^n)/n) - (1, 0)| < r

    sqrt of ((n+1)/n - 1)^2 + (((-1)^n)/n)^2 < r

    Now I assume the n and N come into play, but I don't know how.
  2. jcsd
  3. Sep 24, 2009 #2
    Simply further. You should get something like 2/n^2 under the square root.
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