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Math Help - Is this valid?

  1. #1
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    Is this valid?

    I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

    Let W be an integration from 0 to x.

    We^x = e^x -1
    1 = e^x - We^x
    1 = (1-W)e^x
    1/(1-W) = e^x

    Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

    Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

    Thanks.
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  2. #2
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    Quote Originally Posted by godofgods View Post
    I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

    Let W be an integration from 0 to x.

    We^x = e^x -1
    1 = e^x - We^x
    1 = (1-W)e^x
    1/(1-W) = e^x ***

    Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

    Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

    Thanks.
    I see a problem here ***. The left side of this equation is an operator while the right side is a function of x.
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  3. #3
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    Quote Originally Posted by danny arrigo View Post
    I see a problem here ***. The left side of this equation is an operator while the right side is a function of x.
    But W, which is an integration from 0 to x with respect to x, is the same as x^n/n!. If you change it to that does it rectify the problem?
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  4. #4
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    Quote Originally Posted by godofgods View Post
    I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

    Let W be an integration from 0 to x.

    We^x = e^x -1
    1 = e^x - We^x
    1 = (1-W)e^x
    1/(1-W) = e^x

    Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

    Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

    Thanks.
    Ignore the W and write it out. What you are saying is that: 1 = \left( 1 - \int_0^x \right) e^x dx.
    What is that supposed to mean?
    That looks strange .

    Maybe you can do that in physics but you certainly cannot do that in math.
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