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Weierstrass M-test

  1. Oct 18, 2005 #1
    How do I show that Sigma from 3 to infinity of 1/(n^2+x^2) is uniformly convergent on -infinity< x<infinity using the M-test? Can anyone help? Thanks in advance.
     
  2. jcsd
  3. Oct 18, 2005 #2

    Galileo

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    Well, you need to find terms [itex]M_n[/itex] with [itex]|1/(n^2+x^2)|\leq M_n[/itex] for all x, such that:
    [tex]\sum_{n=3}^{\infty}M_n[/tex] is convergent.

    Looking at your function, does any series come to mind?
     
  4. Oct 18, 2005 #3
    1/n^2? That's what I thought of initially. Is that right and that simple?
     
  5. Oct 18, 2005 #4

    Galileo

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    Why the doubt?
    Is [itex]1/(n^2+x^2)
    \leq 1/n^2[/itex]?
    Is [itex]\sum_{n=3}^{\infty} 1/n^2[/itex] convergent? If so, then according to the M-test your series is uniformly convergent. It's that simple.
     
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