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Difficult Summation Problem Grade 12

  1. Feb 17, 2012 #1
    Determine a formula for the sum of
    [itex]\sum[/itex] iri-1
    in terms of n and r.

    I am stuck on this, i dont understand what to do with the "i" infront of the ri-1


    i know that [itex]\sum[/itex] ri-1 = (1-rn ) /1-r

    all sums are for an index of i=1 to n
    I just don't know how to go any farther. Any help is greatly appreciated. Thanks!
     
    Last edited: Feb 17, 2012
  2. jcsd
  3. Feb 17, 2012 #2

    Dick

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    You don't have any limits on your sum. You should. But here's a hint. The derivative of r^i with respect to r is i*r^(i-1).
     
  4. Feb 17, 2012 #3

    ehild

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    Use that dri/dr=iri-1.

    ehild
     
  5. Feb 17, 2012 #4
    how will finding the derivative of the sum help me find the formula for the sum?
     
  6. Feb 17, 2012 #5

    Dick

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    Define the sum first. If you don't have any limits on it, it doesn't mean anything.
     
  7. Feb 17, 2012 #6
    the sum starts at (i=1) and ends at (n)
     
  8. Feb 17, 2012 #7

    ehild

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    What is the sum Ʃri from i=1 to i=n?


    ehild
     
  9. Feb 20, 2012 #8
    the sum of ri is....

    1-rn
    1-r

    but for the derivative of that i got
    (-nrn-1)(1-r) - (1-rn)(-1)
    (1-r)2

    which is not the correct answer...

    any hints?
     
  10. Feb 20, 2012 #9
    Your sum is incorrect. it should be [1-r^(n+1)]/[1-r] if its from i = 0 to n

    So subtract the term where i = 0 to get the proper sum from 1 to n
     
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