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Sigma notation question

  1. Sep 14, 2015 #1
    1. The problem statement, all variables and given/known data
    http://postimage.org/] Screen_Shot_2015_09_14_at_4_30_06_PM.png [/PLAIN] [Broken]
    image url


    2. Relevant equations
    N/A

    3. The attempt at a solution
    I have to solve a different question using a similar method to this one but I cannot figure out how they got the sigma notation into the last equation format. I tried writing out the summation manually as well as the equation substituting n for 0,1,2,3 but they don't match up and I cannot do my next problem without figuring this one out first.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Sep 14, 2015 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    A little context would be helpful.

    What are α and β? What does u[n] represent?
     
    Last edited by a moderator: May 7, 2017
  4. Sep 14, 2015 #3
    α and β are just variables, there is no value to them in the question. u[n] is a unit step function basically making the function true at n > 0 and 0 at n < 0.

    The original question is a convolution question x[n] * h[n] in linear systems but what is in the picture is all that is really involved. There is nothing else too it I could post.
     
  5. Sep 14, 2015 #4

    Mark44

    Staff: Mentor

    In the summation, you have ##(\frac{\alpha}{\beta})^0 + (\frac{\alpha}{\beta})^1 + (\frac{\alpha}{\beta})^2 + \dots + (\frac{\alpha}{\beta})^n ##, which is a finite geometric series with n + 1 terms. There's a formula for the sum of a geometric series.
     
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