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ReIndexing a Series(non-infinite)

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution
    #7 only
    I'm stumped, i have no idea as to what to do.

    I can't even find help on the internet/book. Its almost like this topic doesn't even exist.

    I know both upper and lower limits have been decreased by 2
  2. jcsd
  3. Jan 24, 2013 #2


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    Ok, then also change k to k+2. Doesn't that make sense? It would offset the other change.
    Last edited: Jan 24, 2013
  4. Jan 24, 2013 #3

    Thank you for responding.

    I understand that part


    I'm just confused as to what to put in the inside.

    I found this on wikipedia. is this relevant?

  5. Jan 25, 2013 #4
    Define a new variable, say, j. How should j and k be related so that j goes from 1 to 6 when k goes from 3 to 8?
  6. Jan 25, 2013 #5


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    Yes, it's relevant .
  7. Jan 25, 2013 #6


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    It's really just an algebraic substitution. The series, as given, starts with k= 3 and we want to change that to a series starting at 1. Rather than use "k" to mean two different things, I am going to call this second index "i". That is, we want i= 1 to correspond to k= 3. That is the same as saying k- i= 3- 1= 2 so that k= i+ 2 or i= k- 2.

    When k= 8, i= 8- 2= 6 so the series goes from i= 1 to 6 as desired. And in the formula for the terms of the series, since, as above, k=i+ 2, replace each k with i+ 2. d What do you get when you replace "k" in "2k- 1" with "i+2"?

    You will get a series in i. Since the "index" is a dummy, and has no meaning in the total sum, you can, to completely match what is required, simply replace "i" with "k" again.
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