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    What is the series sum for:

    0->n , r^4
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    It will be a quintic. Work out 5 values and solve simultaneously.
    Then prove by induction that it really is the formula not just a quintic that works for the first 5 terms.
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    (Original post by Speleo)
    It will be a quintic. Work out 5 values and solve simultaneously.
    Then prove by induction that it really is the formula not just a quintic that works for the first 5 terms.
    Are you sure? Because I am unsure it would work... The sum of a cubic contains only three terms, and the sum of a square does also... Hmm....
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    The sum of squares is a cubic, the sum of cubes is a quartic.
    We may be talking about different things however as your original post makes no sense and I am just guessing what you mean.

    EDIT: actually you need 6 equations if you're doing it properly and not just assuming the constant is zero.
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    (Original post by v-zero)
    Are you sure? Because I am unsure it would work... The sum of a cubic contains on three terms, and the sum of a square does also... Hmm....
    it's gonna be a quintic:

     n^4 + (n-1)^4 + (n-2)^4 + ... + 1
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    (Original post by Speleo)
    The sum of squares is a cubic, the sum of cubes is a quartic.
    We may be talking about different things however as your original post makes no sense and I am just guessing what you mean.
    My point was that solving to find the solution in 5 simultaneous equations may not work, because the equation may not consist of:

    ax^5 + bx^4 + cx^3 + dx^2 + ex .

    Just as the equation for a cubic doesn't consist of:

    ax^4 + bx^3 + cx^2 + dx

    Anyway, bleh, there must be another way - something calculus based...


    But thanks for the ideas!
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    The equation for the sum of cubics does consist of that.
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    (Original post by Speleo)
    The equation for the sum of cubics does consist of that.
    There is no coefficient of x, so not in my view, since zero-coefficients can mess up simultaneous equations.
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    It's still a quartic and no they can't.
    I have the solution and surprise surprise it's a quintic.
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    (Original post by v-zero)
    There is no coefficient of x, so not in my view, since zero-coefficients can mess up simultaneous equations.


    "Not in my view"? I hate to be rude, but the way a quartic polynomial is defined kinda ****s all over your view.
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    (Original post by generalebriety)


    "Not in my view"? I hate to be rude, but the way a quartic polynomial is defined kinda ****s all over your view.
    Still, whether you think that or not is completely null. Zero-coefficients do mess up simultaneous equations.
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    (Original post by Speleo)
    It's still a quartic and no they can't.
    I have the solution and surprise surprise it's a quintic.
    I'm sure it's a quintic, I didn't doubt that. Could you tell me the equation, please?
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    Could you please explain how zero co-efficients mess up simultaneous equations?

    And no do your own homework.
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    (Original post by v-zero)
    Still, whether you think that or not is completely null. Zero-coefficients do mess up simultaneous equations.
    ...

    Well, while I don't have a clue what you're on about and you're clearly being some sort of arse, I should point out that a quintic polynomial will have the form: ax^5 + bx^4 + cx^3 + dx^2 + ex + f. Maybe that's what's causing whatever your imaginary problem is.
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    (Original post by Speleo)
    Could you please explain how zero co-efficients mess up simultaneous equations?

    And no do your own homework.
    It's not my homework, If I wanted to find some sum I could use grapher or mathematica on my mac, I was just trying to work this out earlier, and when I tried my simultaneous equations did not give me the correct answer. It worked for the first five numbers, but not for six, and hence was incorrect.

    But if you don't want to give me the answer then fine.

    Just so you know, I'm not some incapable mathematician coming in here so all you "superior-minds" can do my work for me, I had simply reached the end of my tether with this, and at 3am I thought it might be nice to just know the answer and go to bed. I do not like being belittled by you all - as if I don't know what a quartic or quintic is or how they are defined.

    I have not done FM yet, so my studies in series mathematics have been virtually none (AP and GP series is all). I have C1-C4 and S1-S2, and M1-M2, and I'm doing FP1, FP2 and FP3 along with M3 and M4 before hoping to study maths at university.

    Please, stop being so stupidly stubborn - I wouldn't come to this forum for homework help, because I never need help with any of that, I merely want to attain information beyond my knowledge.


    EDIT: And perhaps I am just tired and am being an idiot, but whenever I do a simultaneous equation to find say the sum of an r^3 series it only works if I have ax^4 + bx^3 + cx^2 . If I add the last two coefficients then I get wrong answers. Like I said, could be (and probably is) tiredness, but I'm at the end of my day and sick of playing.
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    (Original post by v-zero)
    It's not my homework, If I wanted to find some sum I could use grapher or mathematica on my mac, I was just trying to work this out earlier, and when I tried my simultaneous equations did not give me the correct answer. It worked for the first five numbers, but not for six, and hence was incorrect.

    But if you don't want to give me the answer then fine.

    Just so you know, I'm not some incapable mathematician coming in here so all you "superior-minds" can do my work for me, I had simply reached the end of my tether with this, and at 3am I thought it might be nice to just know the answer and go to bed. I do not like being belittled by you all - as if I don't know what a quartic or quintic is or how they are defined.

    I have not done FM yet, so my studies in series mathematics have been virtually none (AP and GP series is all). I have C1-C4 and S1-S2, and M1-M2, and I'm doing FP1, FP2 and FP3 along with M3 and M4 before hoping to study maths at university.

    Please, stop being so stupidly stubborn - I wouldn't come to this forum for homework help, because I never need help with any of that, I merely want to attain information beyond my knowledge.
    All you have to do is work out the first 5 terms of the series (here's one I made earlier 1 17 98 354 979 but check it)
    then solve the 5 simultaneous equations which you get by using an^5 + bn^4 + cn^3 + dn^2 + en = k
    and substituting n = 1, k = 1
    n = 2, k = 17, and so on.


    do you see why this works?
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    (Original post by v-zero)
    EDIT: And perhaps I am just tired and am being an idiot, but whenever I do a simultaneous equation to find say the sum of an r^3 series it only works if I have ax^4 + bx^3 + cx^2 . If I add the last two coefficients then I get wrong answers. Like I said, could be (and probably is) tiredness, but I'm at the end of my day and sick of playing.
    if you add the last two coeffs in there, and write out 5 simultaneous equations, you will find that both turn out to be zero.
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    (Original post by Dirac Delta Function)
    All you have to do is work out the first 5 terms of the series (here's one I made earlier 1 17 98 354 979 but check it)
    then solve the 5 simultaneous equations which you get by using an^5 + bn^4 + cn^3 + dn^2 + en = k
    and substituting n = 1, k = 1
    n = 2, k = 17, and so on.


    do you see why this works?
    This is what I have been doing, I'm pretty sure I just made a mess of things - in either case I don't feel like doing it again.
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    (Original post by v-zero)
    This is what I have been doing, I'm pretty sure I just made a mess of things - in either case I don't feel like doing it again.
    then I suggest you go to bed and have a crack again tomorrow, coz there is absolutely no point someone giving you the answer straight out.
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    (Original post by v-zero)
    It's not my homework, If I wanted to find some sum I could use grapher or mathematica on my mac, I was just trying to work this out earlier, and when I tried my simultaneous equations did not give me the correct answer. It worked for the first five numbers, but not for six, and hence was incorrect.

    But if you don't want to give me the answer then fine.

    Just so you know, I'm not some incapable mathematician coming in here so all you "superior-minds" can do my work for me, I had simply reached the end of my tether with this, and at 3am I thought it might be nice to just know the answer and go to bed. I do not like being belittled by you all - as if I don't know what a quartic or quintic is or how they are defined.

    I have not done FM yet, so my studies in series mathematics have been virtually none (AP and GP series is all). I have C1-C4 and S1-S2, and M1-M2, and I'm doing FP1, FP2 and FP3 along with M3 and M4 before hoping to study maths at university.

    Please, stop being so stupidly stubborn - I wouldn't come to this forum for homework help, because I never need help with any of that, I merely want to attain information beyond my knowledge.


    EDIT: And perhaps I am just tired and am being an idiot, but whenever I do a simultaneous equation to find say the sum of an r^3 series it only works if I have ax^4 + bx^3 + cx^2 . If I add the last two coefficients then I get wrong answers. Like I said, could be (and probably is) tiredness, but I'm at the end of my day and sick of playing.
    We're really not being stubborn. I'm sorry if it comes across that way. But you're being quite rude, you're making ridiculous mathematical propositions and being quite reluctant to tell us what you're on about. Trust us; solving those equations will give you the right answer. If you can't do it, it's probably because it's 3:30am, not because you're stupid.

    Anyway, homework or otherwise, you won't benefit from it if we just give you the answer. We've told you the method and it's one you understand, so if you're having problems with it, tell us what you've done and explain your problem and we'll try and help you further.
 
 
 
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