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!

I Summation algebra

  1. Mar 21, 2016 #1
    Hi, I'm working with series solutions of differential equations and I have come across something that has troubled me other courses as well. given that
    \begin{equation}
    \sum_{n=0}^{\infty} c_{n+2}x^n+e^{-x} \sum_{n=0}^{\infty}c_{n}x^n \\
    \text{where}\\
    e^{-x}=\frac{1}{\sum_{n=0}^{\infty}\frac{x^n}{n!}}\\
    \sum_{n=0}^{\infty} c_{n+2}x^n+\frac{ \sum_{n=0}^{\infty}c_{n}x^n }{\sum_{n=0}^{\infty}\frac{x^n}{n!}}
    \end{equation}
    now my problem is I have the xn in every term and the limits are the same, but I have a fraction of sums and I want to a way to make it simpler. can the xn cancel each other in the fraction. if so
    i then have
    \begin{equation}
    \sum_{n=0}^{\infty} c_{n+2}x^n+ \sum_{n=0}^{\infty} c_n*n!
    \end{equation}
    Is this even allowed?
     
  2. jcsd
  3. Mar 21, 2016 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    No, this is not correct.

    You can see this even by just looking at three terms: there is no reason why
    ##\frac{c_0+c_1x +c_2x²}{1+x+x²/2}=c_0+c_1 +c_2 2##
    would be correct in general.
     
  4. Mar 21, 2016 #3

    Mark44

    Staff: Mentor

    No. Cancelling works when the same factor appears in both numerator and denominator.
     
  5. Mar 21, 2016 #4
    Hi crazycool2:

    NO!

    Take a look at making your cancellation with respect to a similar finite sum.

    (a +bx+cx2) / (1 + x/1 + x2/2) =? (a+b+c)/(1+1+1/2)​

    I understand that this insight will not help you simplify the DE solution you have. I am not sure what kind of simplification you need, but I suggest you start by combining the two sums into one. To do this first rewrite the first sum to be from 2 to ∞.

    Hope this helps.

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: Summation algebra
  1. Summation question (Replies: 3)

  2. Summation Verification (Replies: 6)

  3. Summation question (Replies: 1)

Loading...