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How can this be possible

  1. Nov 25, 2008 #1
    I got this from my Economics lecture notes...

    How come 1 to (n-1) can be split up into [(1 to infinity) minus (n to infinity)]?

    What confuses me is the former one has (n-2) terms, but the latter one has only (n-1) terms...

    And it doesn't make sense to me graphically...
     

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  2. jcsd
  3. Nov 25, 2008 #2

    HallsofIvy

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    The thing that is confusing you is not true. Both sums have n-1 terms.

    Did you try seeing what happens with specific n? If n= 5, the sum from 1 to n-1= 4 is [itex]a_1+ a_2+ a_3+ a_4[/itex]. That has 4= n-1 terms, not n-2.

    The sum from 1 to infinity would be [itex]1+ a_1+ a_2+ a_3+ a_4+ a_ 5+ a_6+ a_7+ \cdot\cdot\cdot+ [/itex] while the sum from n to inifinity is [itex]a_5+ a_6+ a_7+ \cdot\cdot\cdot[/itex]. Subtracting the second from the first leaves [itex]a_1+ a_2+ a_3+ a_4[/itex] as claimed.
     
  4. Nov 25, 2008 #3
    I see! Thank you soooo much!!!
     
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