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Homework Help: Quick question on sums

  1. Nov 4, 2004 #1
    If I have a problem like
    (N) sigma (K=0) Cos(Kpi)

    can I just move the sigma sign inside the brackets? like

    Cos(pi Sigma K)

    just wondering because I have this on an assignment problem and we didn't learn it in class and the text book doesn't cover it either. If I can move it inside the answer is easy so I am just assuming thats how to do it.

    Also, how do you guys write all the math symbols, etc. I see them in other posts but I am pretty much useless on a computer so I have no idea how to do it.

  2. jcsd
  3. Nov 4, 2004 #2

    James R

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    No, you can't just move it inside. For example, consider:

    [tex]\sum\limits_{k=1}^3 \cos(k\pi) = \cos(\pi) + \cos(2\pi) + \cos(3\pi)[/tex]


    [tex]\cos(\pi \sum\limits_{k=1}^3 k) = \cos(\pi(1 + 2 + 3)) = \cos(6\pi)[/tex]

    These are not the same thing.

    (To see how the maths was displayed, click on the displayed equations.)
  4. Nov 4, 2004 #3
    Yeah, I see what your saying. I tried it out after I posted. The problem is I don't have an end number to evaluate it at, but I have a formula for [tex]\sum\ limits_{K=0}^n K[/tex]. I'm thinking because there is no no number to evaluate it at that the answer is just a general formula, like n(n+1)/2 but our text book desn't cover it and we didn't take it in class.
  5. Nov 4, 2004 #4
    sorry about that mess with the sigma sign in the middle, I tried to edit it but it was going to delete it.

    I guess it will take a little practice writting with that stuff.
  6. Nov 5, 2004 #5
    If in doubt of sums, just write out the first terms of the sum in full.
    Sometimes you can see where the sum is heading in infinity...

  7. Nov 5, 2004 #6
    Well you know what you might be interested in this

    [tex]\sum_{r = 0}^{n-1} \cos(\alpha + r\beta) = \cos(\alpha + \frac{n-1}{2}\beta) \frac{\sin(\frac{n\beta}{2})}{\sin(\frac{\beta}{2})}[/tex]

    and you can prove this too :-)

    For your problem, you'd first note that the angles are in arithmetic progression and the above expression would be used with

    [tex]\alpha = 0[/tex]
    [tex]\beta = \pi[/tex]

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