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Math Help - super quick simple question about sigma notation

  1. #1
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    super quick simple question about sigma notation

    I know that the rule is that

    sigma k with n on top of it and k=1 on bottom = 1/2 n(n+1)

    sorry if that is hard to understand but i dont know how to type sigma notation on here

    but i had a problem in one of my calc. problems where it was sigma (k-1) with n on top and bottom as k=1, the answer is 1/2n(n-1)

    I don't understand where the -1 comes from ??? It makes no sense to me

    I tried the problem, I just don't understand it and I have a test tomorrow... please help...thank you
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  2. #2
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    Re: super quick simple question about sigma notation

    I'm not sure whether it's the notation that's giving you trouble, or the formula in n that equals the sum. See the attached pdf that I hope will help you with the notation. I'm also including another pdf which I got from Purplemath. It will show you a method by which these formulas may be derived.

    I'm not so good at entering this notation either. It's not so hard, but I've been lazy. There's a forum and some guidance elsewhere on this site about how to use latex.

    Just had a thought ... that pdf I sent you from Purplemath ... just in case you don't see how to apply the method ...

    It's true that she's talking about sequences, not series. Well, think of the series represented by the sigma k as a sequence of partial sums. What are the partial sums? You can count them starting at 0 or at 1. If you start at 0, they're 0, 1, 3, 6, 10, 15, 21 ... but if you start at 1 they're 1, 3, 6, 10, 15, 21 ... now set up the simultaneous equations the way she describes and you'll see you arrive at two different formulas.

    Hope this helps.
    Attached Files Attached Files
    Last edited by zhandele; April 22nd 2013 at 06:57 PM. Reason: afterthought
    Thanks from laurenboboren
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  3. #3
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    Re: super quick simple question about sigma notation

    Thanks, the formula wasn't in my textbook for some reason, I don't really quite understand it but I'll think I'll just try to memorize the formula for the test
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  4. #4
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    Re: super quick simple question about sigma notation

    I just checked your profile, I gather you're taking calc I now.

    I thought I'd tell you something that I wish somebody had said to me when I was at the stage where you are.

    When you learned about derivatives, you probably heard the word "differentiation." Did anyone explain why finding the derivative is called "differentiation"? It means finding the differences between successive elements in a sequence. You're really talking about sequences, not continuous functions. The connection between sequences and functions is the notion of limit, that is, a continuous function is like a sequence with such a large number of elements we can't count them all.

    Now if you take those partial sums

    0 1 3 6 10 15 21 ...

    and then the differences between successive sums

    1 2 3 4 5 6

    this is the "first differentiation," or "the first derivative," and if you do it again

    1 1 1 1 1 ...

    You have a constant. It's just like x^2 and you differentiate (take the derivative to get) x, then x and you differentiate to get 0. Finding this formula is like integration.

    I don't know if I'm doing a good job here. But don't worry. All math is simple, once you get it.
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  5. #5
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    Re: super quick simple question about sigma notation

    LaTeX is pretty easy to use. If you put your mouse over someone else's figure, it shows the code he used. You need to put [ T E X ] before it and [ / T E X ] after it (removing the spaces). Here's an example of a sum:

    \sum_{n=0}^\infty \frac{(-1)^{2n+1}x^{2n+1}}{(2n+1)!}

    - Hollywood
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