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Help with series math problem

  1. Dec 24, 2004 #1
    I'm just not so sure on how to approach this problem. Well, here it goes:

    [tex] \sum _{n=1} ^{\infty} \left[ \tan ^{-1} (n+1) - \tan ^{-1} (n) \right] = \frac{\pi}{2} [/tex]

    I know that

    [tex] \tan ^{-1} x = \sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{x^{2n+1}}{2n+1} [/tex]

    but I don't know if it can be useful to get to the answer above. I just need some tips. Any help is highly appreciated.
    Last edited: Dec 24, 2004
  2. jcsd
  3. Dec 24, 2004 #2


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    Try writing out the first few terms.

    P.S. I get [itex]\pi/4[/itex].
  4. Dec 24, 2004 #3
    Oh... I see. By the way, you're right about the [itex]\pi/4[/itex].

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