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T = 64/(165+3n) finite sum

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data

    I want a general equation for the finite sum of n0 + n1 + n2... starting at n = 0 for the equation t = 64/(165+3n) so i have a sum of numbers: 64/165 + 64/168 + 64/171...

    i don't want you to think i am lazy and don't show work but this isn't for school. i want to figure out how much time having passed on a very long recording of a metronome corresponds to the beats per minute being played.

    1 bar = 4 beats
    start at 55% of 300 beats per minute
    after 16 bars have passed it starts over but 3 beats per minute are added to the speed.
    so it goes from 165 beats per minute to 168 to 171...

    i could just add them all up and make a little reference table but i am determined now to understand how to solve this problem!

    2. Relevant equations

    t = 64/(165+3n)

    3. The attempt at a solution

    my attempts are all useless.
     
    Last edited: Nov 12, 2009
  2. jcsd
  3. Nov 12, 2009 #2
    Can you express it as:
    [tex]\frac{64}{3}\sum_{n=0}^{i}\frac{1}{55+n}[/tex]
    Such that :
    [tex]i \geq n[/tex]
    [tex]i \in\mathbb{Z}^{+}[/tex]
     
    Last edited: Nov 12, 2009
  4. Nov 12, 2009 #3

    Gib Z

    User Avatar
    Homework Helper

    Welcome to PF!

    So when you say "finite" sum, are you summing a finite amount of terms, or summing an infinite number of terms but want a finite result? Because the sum is actually divergent ie it does not sum to any finite number.

    If you are however summing a finite number of terms, even a large amount, it can be done exactly by some Mathematics Program such as Maple or Mathematica, or approximated quite well with some simple analysis.
     
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