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!

Summation Question (Properties)

  1. Dec 2, 2004 #1
    I have a rather simple question, but my rusty brain needs a good, swift kick-start.

    I start with:

    [tex]\sum_{i=1}^k i[/tex]

    and substitute in [tex]i=k-j[/tex] to get:

    [tex]\sum_{k-j=1}^k (k-j)[/tex]

    How do I get from this to the following?

    [tex]\sum_{k-j=1}^k (k-j) \rightarrow \sum_{j=0}^{k-1} (k-j)[/tex]

    Thanks in advance for your help.

    Last edited: Dec 2, 2004
  2. jcsd
  3. Dec 2, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You're in some confusion in how to interpret the summation limits.
    Let's write it explicitly, to see how it follows:

    Now, rearrange the inequalities in the last expression:
    Which in standard notation is nothing else than:
    Last edited: Dec 2, 2004
  4. Dec 2, 2004 #3
    Thank you!

    I completely understand now. I just need a good, swift kick. :tongue2:

    Thanks again and take care!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Summation Question Properties Date
Summation question Jan 9, 2016
Summation question Jan 20, 2014
Question regarding Einstein's summation convention! Jan 15, 2012
Summation question May 15, 2010
Summation Question Nov 10, 2007