Haim
Posts:
8,795
Registered:
12/6/04


Series
Posted:
Sep 20, 2008 3:31 PM


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

