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Thread: Need Reference to Math Info ( Series and Sequences )

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    $3n10r M3mb3r defcon's Avatar
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    Need Reference to Math Info ( Series and Sequences )

    Hey.. finals coming up :P i was wondering if anyone here know where i could get a site that lists all the types of series and how to test for their convergence/divergance.

    Also, is there any site that you know of that gives you sum tips on finding the general term of a sequence. thanx in advance.


    EDIT: Not doing Fourier series, and i alrdy chked yahoo, can';t find nothing worth my time :P
    Last edited by defcon; 11-29-2003 at 02:12 PM.

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    $3n10r M3mb3r defcon's Avatar
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    thanx.

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    One crazy MOFO/Mail man
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    Correct me if I am wrong but are there really only 2 ways to check for convergence? They are just a proccess you go through to find them. If you can do some you can pretty much do them all....

    Fourier series convergence is another animal totally. I don't like it one bit.
    w00t

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    $3n10r M3mb3r defcon's Avatar
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    Not doing fourier, that comes next semester.. But what we aare doing now goes like this.

    1. We are given a Sum from 1 to infin of the term An( n is subscript ).

    2. The queston wants us to discuss the if this term diverges, converges, if it does converge, does it converge absolutly or conditionally.

    We were introduced to several tests in class that we use to evaluate this general term ( most use limits, and depending on what the limit of the general term is, we get if it diverges or converges. ) The tests we used in class were..
    (i) The nth term test
    (ii) The geometric series test
    (iii) The integral test
    (iv) The comparison tests
    (v) The alternating series
    (vi) The ratio test
    (vii) The root test

    There may be a way, or test that works for all general terms.. but we were not introduced to it.. ( profs would do that wouldn;t they :P ) How would you approach a question that asked us to evaluate the general term? let me look up an example for ya.

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    One crazy MOFO/Mail man
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    When I get home I will give you the 2 tests that work every time (I think because that's the only 2 we ever used on any question. Both could be used one is easier then the other in some cases though). I'm at school right now so... when I get home... I'm actually studing fourier transform right now :P
    w00t

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    $3n10r M3mb3r defcon's Avatar
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    haha, sucks for you :P im studying mechanics.. finding the centroids of volumes of different density. Not to fun if you ask me :P
    Last edited by defcon; 11-30-2003 at 07:08 PM.

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    $3n10r M3mb3r defcon's Avatar
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    Hey GP.. I was wondering.. could you give me a "physical" description of what it actually means when a series "converges"?

    That is sumthing ive never really understood.. and hence this is the only part of the math course i do not understand fully. i could memorise all the tests n such and apply them no prob.. but that is pretty much useless once the final exam is over..

    So If possible.. what does it mean when a series converges? graphical representation.. anything.

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    One crazy MOFO/Mail man
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    Well the physical representation or graphical rep is kind of weird. In the end you just want to know of the sumation of the signal (or equation or series or what ever you want to call it) over all possible values (-iv inf to inf) is bounded. If there is a DC term in your signal then the summation of the signal will diverge -> summation will go to inf. Because as you go to inf you will always continue to sum that DC term over and over and over. If not then as you sum (or in the continuous version integrate) the sum will be bounded by some constand B. All those tests just try to tell you if this "B" exsists. The only place you use this stuff is really in geometric series convergence...
    w00t

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    $3n10r M3mb3r defcon's Avatar
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    i think i get what your saying.. meh.. i'll jus have to work on it :\

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    Asshole. SuperFlex's Avatar
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    a(n-1)d.

    Where:
    a = first term
    n = nth term
    d = difference between terms.

    This is for a numerical series i think. Can't remember the one for a geometric series.
    Asshole.

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    WannabeBUFF Member buffzilla's Avatar
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    $3n10r M3mb3r defcon's Avatar
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    buff, i just stumbled across that site like earlier today haha, it has lots of infomation on it thanx.

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    hmm, I like to be big!!!
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    umm I think he means physical like a real world representation

    Like if you drop a ball and it always comes back to half it's original height, it will bounce an infinite amount of times, but over a finite time period.

    The sequence would look like H+2H/2+2h/4+2h/8.......


    If you need help with problems I can most likely help you pretty easily, I rock at series.
    Chris Mason is my master.....

    American cars are like fat people, sure, they have a lot of power, but they're not built well, and they have all that useless weight, plus they make both make funny noises.

    feel free to aim me, nejar462 im on a lot. Don't know much to warn you dudes, but im good at conversations.

    Belial in reference to Ronnie Coleman, "Some people say he still has blood in his steroid stream, but I doubt it. Gas isn't one of the side effects, but that massive bloated overly muscular freak of nature circus sideshow appearance might be what tips most people off."

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    $3n10r M3mb3r defcon's Avatar
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    Originally posted by nejar462
    umm I think he means physical like a real world representation

    Like if you drop a ball and it always comes back to half it's original height, it will bounce an infinite amount of times, but over a finite time period.

    The sequence would look like H+2H/2+2h/4+2h/8.......


    If you need help with problems I can most likely help you pretty easily, I rock at series.
    Yeah.. thats what i mean.. but i still can't picture it.. you plot a graph of bounce vs time.. and you say time is limited.. then how can the bounce be infinite? it will only keep bouncing increasingly small intervals until it reaches that limited time.. bleh! i hate this stuff :P

    The biggest problem i have with them, is recognizing which "general series form" the question is.. you know what i mean? I have trouble simplifying the expression down to a recognizable form

    Here is an example, what method would you use to reduce this?

    SUM from n=(4 to infinity) of the term ( n-3 ) / ( n^3 - 3n^2 - 4n + 12 )

  16. #16
    hmm, I like to be big!!!
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    umm, that'll definetly converge, is that all you're asked to do, because I don't have the knowledge to sum that, unless you want to use the integral test, which'll only give u bounds...

    just consider the largest term of N, and use that
    Chris Mason is my master.....

    American cars are like fat people, sure, they have a lot of power, but they're not built well, and they have all that useless weight, plus they make both make funny noises.

    feel free to aim me, nejar462 im on a lot. Don't know much to warn you dudes, but im good at conversations.

    Belial in reference to Ronnie Coleman, "Some people say he still has blood in his steroid stream, but I doubt it. Gas isn't one of the side effects, but that massive bloated overly muscular freak of nature circus sideshow appearance might be what tips most people off."

  17. #17
    One crazy MOFO/Mail man
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    divide everything by the highest order of n which is n^3 and you will clearly see it goes to 0.
    w00t

  18. #18
    One crazy MOFO/Mail man
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    since as n aproaches infinity the n^3 term dominates the expression.
    w00t

  19. #19
    hmm, I like to be big!!!
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    you can also use sequences and series for compound interest equations.
    Chris Mason is my master.....

    American cars are like fat people, sure, they have a lot of power, but they're not built well, and they have all that useless weight, plus they make both make funny noises.

    feel free to aim me, nejar462 im on a lot. Don't know much to warn you dudes, but im good at conversations.

    Belial in reference to Ronnie Coleman, "Some people say he still has blood in his steroid stream, but I doubt it. Gas isn't one of the side effects, but that massive bloated overly muscular freak of nature circus sideshow appearance might be what tips most people off."

  20. #20
    Senior Member Trent_Steel's Avatar
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    I don't know of any sites, but a great maths book is Mathematical Methods in the Physical Sciences by Boas. There is a great chapter on series in there. It was kind of the maths bible when I was doing stuff like that in college.
    Last edited by Trent_Steel; 12-06-2003 at 05:36 PM.

  21. #21
    $3n10r M3mb3r defcon's Avatar
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    Math test is over.. It went Semi Fine, sum weird questions, but overall not bad. I will not post until Dec. 13th

    This week is crazy

  22. #22
    One crazy MOFO/Mail man
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    Quote Originally Posted by defcon
    Math test is over.. It went Semi Fine, sum weird questions, but overall not bad. I will not post until Dec. 13th

    This week is crazy

    Yeah I got destroyed on my Linear signals exam.
    w00t

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