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Sigma Notation


Date: 4/14/96 at 3:16:17
From: tnicpwr
Subject: sigma notation

Dear Dr Math,

I am trying to find questions regarding sigma notation.  For 
example: (with the sigma notation sign in front)5+6r, (with the 
sigma notation sign in front)r(r+1). 

  Thank you.


Date: 4/14/96 at 14:47:47
From: Doctor Syd
Subject: Re: sigma notation

Hello!

I'm not quite sure what you are looking for... you want questions 
regarding sigma notation?  Are you curious about infinite series 
and the convergence/divergence of series?  I'm not sure in what 
direction your question is going.  But, since you asked for 
questions regarding sigma notation, I'll give you one:

For this question let {E n=0 to n=infinity} denote the sigma with 
values of n going from 0 to infinity.

Calculate:  E n=0 to n= infinity ( ar^n), where a and r are 
constants.  

This is an example of an infinite series.  You'll find that 
depending on the value of r, sometimes it converges (this means 
the sum is a finite number), and sometimes not.  

I don't know if you've worked with infinite series before, or only 
finite series, but infinite serious have fascinated mathematicians 
for a long time.

Another famous infinite serious is called the harmonic series: 

E n=1 to n= infinity 1/n

This series actually diverges (the sum goes to infinity) even 
though the terms in the end of the sum get really small.  Pretty 
neat, eh?  See if you can prove why.  It involves a trick of 
sorts, but try to think about it!  

I hope this helps.  If I didn't answer your question, write back 
and re-ask it in different terms.

-Doctor Syd,  The Math Forum

    
Associated Topics:
High School Sequences, Series

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