Question 1117531
<font face="Times New Roman" size="+2">


Step 1:  Plain text notation lesson.  <b>sum[1,infty] -4(-1/2)^(n-1)</b> would be interpreted as 



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{n=1}^\infty\,-4\(-\frac{1}{2}\)^{n-1}]


2. Convergence:  A geometric series converges if the common ratio *[tex \Large r] is in the interval *[tex \Large -1\ <\ r\ <\ 1].  Since  *[tex \Large -1\ <\ -\frac{1}{2} <\ 1], this series converges.


The sum of a convergent geometric series of the form


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{n=0}^\infty\ ar^n\ =\ \sum_{n=1}^\infty\ ar^{n-1}]


is given by


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a}{1\ -\ r}]


The rest is just arithmetic.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 

</font>