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Series notation and commutativity

  1. Nov 21, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm trying to wrap my head around series notation, but I'm finding some of the transformations hard to grasp. For example, this one:

    2. Relevant equations
    [itex]\Sigma^{n}_{i=1} (2a_{i}-3) = 2\Sigma^{n}_{i=1}a{_i}(-3n)[/itex]

    3. The attempt at a solution
    In the above expression, I don't understand how you end up with -3n on the RHS. Why can't it just be left as -3?
     
  2. jcsd
  3. Nov 21, 2013 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Actually, that is the definition of multiplication!

    [itex]3n = \overbrace{3 + 3 + ... + 3}^{n \ times} \ = \ \sum_{i=1}^n3[/itex]
     
  4. Nov 21, 2013 #3

    Mark44

    Staff: Mentor

    ##\sum_{i = 1}^n (2a_i - 3) = \sum_{i = 1}^n 2a_i - \sum_{i = 1}^n 3##

    The last sum is 3 + 3 + 3 + ... + 3, a sum with n terms.
     
  5. Nov 21, 2013 #4
    Great replies thank you both!
     
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