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Limit of sum, sum of limit

  1. Feb 1, 2010 #1
    For an infinite sum, is the limit of the sum = sum of the limit?
    lim_{x \rightarrow a} \sum_{n=0}^\infty f(x,n)= \sum_{n=0}^\infty lim_{x \rightarrow a}f(x,n)
  2. jcsd
  3. Feb 1, 2010 #2
    I'm fairly certain that it's true if and only if
    \sum_{n=0}^{\infty} f(x,n)

    converges uniformly. In general, however, no.
  4. Feb 2, 2010 #3
    Thank you L'Hopital!!!
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