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Finite geometric series formula derivation? why r*S??

  1. Feb 4, 2016 #1
    what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure
     
  2. jcsd
  3. Feb 4, 2016 #2

    Samy_A

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    The "rationale" is that it works.

    Why wouldn't that operation be valid?
    What he basically does is:

    ##a=b+c+d+e##
    ##f=\ \ \ \ \ \ c+d+e+g##
    then, subtracting the second equation from the first gives ##a-f=b-g##

    The other terms cancel each other.
     
  4. Feb 4, 2016 #3
    i get that it works, but the closest logical explanation i have for myself is 1 - (r^n) divided by 1 - r is the polynomial 1 + r + r^2 + ... + r^(n-1) + r^n. which is identical to the finite geometric series. Thus, distributing (1 - r) to the polynomial gives us 1*S -r*S = S - rS.
     
  5. Feb 5, 2016 #4

    Samy_A

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    I see.
    Yes, that is correct.
     
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