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How Can I Make This Simpler?

  1. Jun 15, 2010 #1
    I have the following equations:

    (See Figure 1)

    I tried summing them up in one single general formula, and I got:

    (See Figure 2)

    I'd like to know two things:

    1. Is my general formula correct? Please note it does not work for A1, since for my purposes, A0 does not exist.

    2. If my formula is correct, how can I make it simpler, so I can computate An by hand?

    Thank you very much for your help! I'm sure this is gonna be simple, but my knowledge is limited.
     

    Attached Files:

  2. jcsd
  3. Jun 16, 2010 #2
    1. Your equation is indeed correct. But I prefer to write it this way:
    [tex]A_n=A_{n-1}y+A_1x[/tex]

    2. If you want to make it simple and compute it by hand, I guess you would like to solve the above difference equation. Here is the solution:

    [tex]A_n=A_1y^{n-1}+A_1x\left(\frac{y^{n-1}-1}{y-1}\right)[/tex]

    Please refer to this http://www.voofie.com/content/77/general-term-of-recurrence-relation-and-its-solution/" [Broken], if you are interested in how to get the answer. With this equation, I think you can compute any term by hand easily.
     
    Last edited by a moderator: May 4, 2017
  4. Jun 17, 2010 #3
    Thank you very much, that was very helpful!
     
  5. Jun 20, 2010 #4
    You are welcome. Is it some kind of homework problem? Or you encounter it in your self-study?
     
  6. Jun 21, 2010 #5
    Just a problem that arose while studying some experiments. Not homework related. Thank you again.
     
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