1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ReIndexing a Series(non-infinite)

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

    reindex.jpg

    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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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
    Hello,

    Thank you for responding.

    I understand that part

    6
    sigma
    1

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

    I found this on wikipedia. is this relevant?

    e3114b84602343dddffd631e9abd9047.png
     
  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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: ReIndexing a Series(non-infinite)
  1. Infinite series (Replies: 4)

  2. Infinite Series (Replies: 2)

  3. Infinite series. (Replies: 4)

  4. Infinite series. (Replies: 1)

Loading...