Yes, also useful to show that the sequence of *differences* in
a 2nd power series is linear e.g.
1 4 9 16 25 <-- n^2
\ / \ / \ / \ /
3 5 7 9 <-- additive 2
and the *differences* between terms in a 3rd power series
is a 2nd power e.g.
1 8 27 64 125
\ / \ /\ /\ /
7 19 37 61 <-- n^3 - (n-1)^3 or 3n^2 - 3n + 1 (n=2,3..)
and so on. Good background for appreciating calculus:
D(x^n) -> n x^n-1 i.e. derivative relates to differences, and
you drop a power (exponent degree down by one) with each
successive differentiation (note term embeds concept of "difference").
Note: reverse differentiation is integration, getting a running
total of differences, which takes you up one power with each
application. Integrate linear to get areal (2nd power), integrate
again to get volumetric (3rd power).
For more along these lines see:
http://www.inetarena.com/~pdx4d/ocn/calculus1.html
>>>>> The plural of mongoose begins with p. <<<<
>
>P.S. The concept corresponding to _slope_ is actually _base_, isn't it?
> Or would it be the _log_ of the base?
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