Infinite Series: A Beginner's Guide

[vigintitres]

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

 

[mathman]

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.

 

[Focus]

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.

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.

 

[ZharAngel]

<br /> T_n = ar^{n-1}<br />

<br /> r &lt; 1<br />

<br /> S_n = \frac{a(1-r^n)}{1-r}<br />

<br /> n \rightarrow \infty<br />

<br /> r^n \rightarrow 0<br />

<br /> S_\infty = \frac{a}{1-r}<br />