I am a subversive.

[unixronin]

Yes, I admit it!  Freely!  Proudly, even!

I, you see, just taught Goose to sum arbitrary geometric and arithmetic series.

She's nine years old, and in fourth grade.

Her teachers are going to hate us, if she hasn't forgotten it by the next time she comes to a number series problem.

Comments

[rbos.livejournal.com]

hm. I don't even remember how to do that. :)

unless you mean something like sigma(i=x..y)(f(i)) ?

[unixronin.livejournal.com]

I think we're talking about the same thing, yes. Sum of first and last desired terms, times number of terms, divided by two.

[rbos.livejournal.com]

oh. I guess that would work for linearly-increasing series. Not arbitrary ones, though.

[unixronin.livejournal.com]

Aha. I think we're using a different definition of "arbitrary".

I'm using "arbitrary [arithmetic or geometric] series" to mean "[arithmetic or geometric] series whose terms can be defined as some arbitrary function on the ordinal number of the term."

I infer that you were interpreting it as "series whose terms are not defined by any deterministic mathematical function." In other words, just a series of unconnected values. There's no way to accurately sum such a series of values except by just doing the addition, though I suppose one could approximate the sum (to a specified degree of confidence, within specified margins of error) by statistically sampling a well-chosen subset of the terms.