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.

[eleazar.livejournal.com]

Huzzah!, if they let her keep it. We need more subversives.

(As I recall, it was around fourth grade that I got taught how to not multiply n digit numbers in my head.)

[ilcylic.livejournal.com]

I'm reminded of a couple years ago when I was forced, as part of my welding curricula, to take "Math For Welders". Yes, this was every bit as bad as you might imagine. It started out with basic addition and subtraction. Multiplication and division each got their own week of study.

As someone with a degree who has taken and passed Calc 2, it was a bit low. (And for some ungodly reason TVI wouldn't accept transfer credits from UNM.)

"You have to show your work, Ogre."

"I don't even remember how to show my work on long division, sir."

"What are you going to do if you have to work out some length in the field?"

"Use the calculator in my phone."

-Ogre

[unixronin.livejournal.com]

yeah, been there, done that. I hated showing my working on simple things when I was in school ... it meant I had to slow down my thinking to the speed I could write at.