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How is this equality possible? What did the professor do to reach it?

  1. Mar 8, 2012 #1
    1EC5D0B7C.png


    Can someone explain me how one term got to the other term? It makes no sense to me
     

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  3. Mar 8, 2012 #2

    NascentOxygen

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    Staff: Mentor


    Your image is not publicly accessible. Can you change its permissons?
     
  4. Mar 8, 2012 #3
    I uploaded it.

    By the way, he said something about "factoring sums out" what is that supposed to mean? This is the first time i've ever encountered something like this and i have taken up to differential equations regarding my math level.
     
  5. Mar 8, 2012 #4

    NascentOxygen

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    The expression is of the form: A. ln Q - A. ln w
    where A is a long summation and common to both terms.

    Besides A, ln Q is the other term inside the first summation (likewise, besides A, you can see that ln w is the other term in the second series).

    As each summation is over the same range, then you can combine the two series in one, using just one sigma.

    Then combine the terms into one making use of: ln Q - ln w = ln (Q/w)

    finally remember: ln (Q/w) = - ln (w/Q)

    It looks forbidding, but really isn't. :wink:

    Basically, write the expression without the ∑ symbol, and simplify what you see.

    EDITED
     
    Last edited: Mar 8, 2012
  6. Mar 8, 2012 #5
    i'm so stupid.. i deserve to go start college again.. Thanks a lot man!


    (honestly, i didnt know you could combine two same series into one, i was just treating them as a normal number and they were cancelling each other or getting a sigma squared, lol)
     
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