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Topic: Series
Replies: 25   Last Post: Sep 24, 2008 9:29 PM

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Haim

Posts: 8,239
Registered: 12/6/04
Series
Posted: Sep 20, 2008 3:31 PM
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Kirby Posted: Sep 19, 2008 11:05 AM

>2.7182818284590451
>
>Yes it's just an approximation but that's not the problem
>for us that it is for some people. We have the usual
>segments with the infinite series (...) for people that
>want and/or need them for some reason.


Kirby,

Your comment prompted me to think about a topic that has not been on my mind for a while. The usual first step in teaching mathematics to small children is to teach the addition of arbitrary terms. We have them work out sums like,

(1) S = 3+15+8+162+...

The usual next step is to investigate what clever things we can do when the terms of the sum are identical, such as,

(2) S = 3+3+3+....

After a while, we relax this restriction by no longer requiring the terms of the sum to be identical, but we still require a constant difference between the terms, such as

(3) S = 1+3+5+7+...

This is an example of a series with constant difference, d=2, and we recognize (2) as as a series with constant difference, d=0.

Well, I know that (1) is general addition. And I know that (3) is an example of an arithmetic series, for which we have a couple of closed form equations for arbitrary constant differences. But, I wonder what we should call (2). Do you think Professor Keith Devlin might have a suggestion?

Haim
Unashamedly White and Unapologetically Jewish



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