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Infinite series

  1. Aug 3, 2008 #1
    I am getting into this topic and I am having a hard time conceptualizing it. Is there anybody that can spend a minute letting me know the "reality" to infinite series? By that I mean, please explain infinite series in such a way that a beginner like me will be able to take what you said and apply it to home work problems. Thanks and if I am asking too much I understand because this is a deep topic
     
  2. jcsd
  3. Aug 3, 2008 #2

    mathman

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    Gold Member

    I don't know what you mean by reality. However a simple example is:

    1 + 1/2 + 1/4 + 1/8 +1/16 + etc. where you never stop. As a result it adds up to 2.
     
  4. Aug 3, 2008 #3
    You can think of this as taking half a step as you did last step. Your first step is of 1 unit, so next step is 1/2, next one 1/4 and so on. The question is how much distance can you travel using this method and that is 2. You cannot exceed 2 units of distance by using this mode of transportation.
     
  5. Aug 4, 2008 #4
    [tex]
    T_n = ar^{n-1}
    [/tex]

    [tex]
    r < 1
    [/tex]

    [tex]
    S_n = \frac{a(1-r^n)}{1-r}
    [/tex]

    [tex]
    n \rightarrow \infty
    [/tex]

    [tex]
    r^n \rightarrow 0
    [/tex]

    [tex]
    S_\infty = \frac{a}{1-r}
    [/tex]
     
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