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!

How to multiply these summations ?

  1. Nov 20, 2011 #1
    Ok. I feel a little dumb for asking, but I'm working on a abstract algebra proof and this has got me stuck:

    [itex]\left(\sum_{i=1}^{n}a_ib_i\right)\left(\sum_{i=1}^{k}a_ib_i\right)[/itex] where n,k are some positive integers.

    I feel certain that it's not just a sum to n+k or nk, but I could be wrong. any help would be awesome. :)
     
  2. jcsd
  3. Nov 20, 2011 #2
    It can be written as a single sum with the cauchy product.
    The terms of the new series are the convolution of the original terms.

    An elementary way to see it is: attach x^i to each coefficient, then group in a single series in powers of x, then put x=1.
    Like you would do for (1 + x + 3 x^2)(2 + x + x^2)= (1+2) + (1*2+1*1)x + (3*2+1*1+1*1)x^2 + ...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to multiply these summations ?
Loading...