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### Sigma Notation

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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

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
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

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Associated Topics:
High School Sequences, Series

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