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Math Help - Create sum expression from algebraic expression

  1. #1
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    Create sum expression from algebraic expression

    Hello,

    I am trying to create a summation equation from this algebra equation, would it be possible?

    x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x

    If so can anyone help me?
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  2. #2
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    re: Create sum expression from algebraic expression

    Strictly speaking, this is not an equation because it lacks the = sign. It's an expression. If by "summation equation" you mean an expression that uses the \sum symbol, then

    x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x=\sum_{i=1}^{11}(  ix)

    If you want to simplify that expression, then you can use the formula for the sum of an arithmetic progression:

    x+\dots+11x=(1+\dots+11)x=\frac{11\cdot12}{2}x=66x
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  3. #3
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    re: Create sum expression from algebraic expression

    Thank you for the response, I understand that in order to create the equation that symbol is needed but my question is would it be possible to convert the equation I posted into that summation? if so how?

    basically it works by set periods for example if the period is set to 3 then the equation would be: x+2x+3x and if the period is set to 4 then the equation would be x+2x+3x+4x
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  4. #4
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    re: Create sum expression from algebraic expression

    x+2x+\dots+nx=\frac{n(n+1)}{2}x

    Edit: If this is not what you want, please explain what you mean by "that summation."
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  5. #5
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    re: Create sum expression from algebraic expression

    Hello,

    Yes I needed a formula and that one is good. I guess I was thinking that the formula could have been written using the summation symbol?
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  6. #6
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    re: Create sum expression from algebraic expression

    The formula with the summation symbol is given in post #2 (you can replace 11 with n and add ... in the left-hand side).
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  7. #7
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    re: Create sum expression from algebraic expression

    I haven't dealt with calculus in a while, thank you very much.
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  8. #8
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    Re: Create sum expression from algebraic expression

    Hello,

    I wanted to ask if I got these written correctly:

    900: 1x+2x+3x+4x+5x+6x+6x+6x+6x+6x+6x+6x
    500: 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x
    100: 1x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x+12x

    For these would the equation be correct written:

    900: S (upper: 5 lower: 1) ix + S (upper:6 lower: 1) 6x where x = 10000
    500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000
    500: S (upper: 12 lower: 1) ix where x = 10000
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  9. #9
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    Re: Create sum expression from algebraic expression

    I don't see the relationship between 900, 500, 100 and the expressions after the colon.

    In this forum, you can write [tex]\sum_{i=1}^{12} ix[/tex] to get \sum_{i=1}^{12} ix.

    Below \sum (capital Greek sigma) we typically write i = 1, not just 1, but above \sum we write just 12 (for example). The notation \sum_{i=1}^{12} means the sum where i ranges from 1 to 12.

    500: S (upper: 12 lower: 1) ix where x = 10000
    \sum_{i=1}^{12}ix is indeed 1x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x+12x regardless of the value of x.

    500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000
    1x+2x+3x+4x+5x+6x+7x=\sum_{i=1}^7ix. To represent 8x+8x+8x+8x+8x you can write \sum_{i=8}^{12}8x, or \sum_{i=1}^{5}8x (note that there is no i after \sum, which means that all terms in the sum are the same), or just 5\cdot 8x.
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  10. #10
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    Re: Create sum expression from algebraic expression

    The 500, 900 is labeling. but are the calculations correct?
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  11. #11
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    Re: Create sum expression from algebraic expression

    Quote Originally Posted by silver163 View Post
    but are the calculations correct?
    No.

    Quote Originally Posted by silver163 View Post
    900: 1x+2x+3x+4x+5x+6x+6x+6x+6x+6x+6x+6x
    ...
    900: S (upper: 5 lower: 1) ix + S (upper:6 lower: 1) 6x where x = 10000
    In the explicit sum, 6x occurs 7 times, but in the sigma-expression, it is used only 6 times.

    Quote Originally Posted by silver163 View Post
    500: 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x
    ...
    500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000
    It is not clear what 6x is doing in the sigma-expression and why you have \sum_{i=7}^5ix, where the upper limit is less than the lower one.
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  12. #12
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    Re: Create sum expression from algebraic expression

    so would it be correct:

    \sum_{i=1}^6ix

    ?
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  13. #13
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    Re: Create sum expression from algebraic expression

    This is not an equation (it does not have an = sign), so I can't say if it's true or false.
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  14. #14
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    Re: Create sum expression from algebraic expression

    ok is this statement true?

    \sum_{i=1}^6ix+ \sum_{i=1}^58x = 680000
    Last edited by silver163; January 14th 2012 at 02:09 PM.
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  15. #15
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    Re: Create sum expression from algebraic expression

    \sum_{i=1}^6ix+\sum_{i=1}^58x=\left(\sum_{i=1}^6i+  \sum_{i=1}^58\right)x=(21+40)x=61x. However, in post #8 the expression labeled 500 has 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x = \sum_{i=1}^7ix+\sum_{i=1}^58x = 28x+40x = 68x, which is indeed 680000 for x = 10000.
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