Limit of sum, sum of limit

  • #1
202
0
For an infinite sum, is the limit of the sum = sum of the limit?
ie.
[tex]
lim_{x \rightarrow a} \sum_{n=0}^\infty f(x,n)= \sum_{n=0}^\infty lim_{x \rightarrow a}f(x,n)
[/tex]
 

Answers and Replies

  • #2
258
0
I'm fairly certain that it's true if and only if
[tex]
\sum_{n=0}^{\infty} f(x,n)
[/tex]

converges uniformly. In general, however, no.
 
  • #3
202
0
Thank you L'Hopital!!!
 

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