Infinite Series

Something I just noticed–– linear and quadratic infinite series almost always total to infinity or negative infinity. When I say linear, I mean in the form (an+b) or in standard form for quadratics. Anyway, it depends on the coefficient of the highest degree of n–- every time.

There are a lot of good math You-Tubers: Vihart and Numberphile are two of my particular favorites, Vihart in particular being particularly kid-friendly. Her "Doodling in Math Class" videos are some of my favorites.

In one of her videos, she argues with the plural of series. I think it should be 'serieses', as the plural of proper nouns is (Not to be one of those Gollumses). However, some singular nouns ending in one -s double the 's' and add -es instead. However, those nouns have a hard 's' as in 'cross' rather than the soft one in 'has'... well, frankly, I don't care too much.

We learned something cool in math class the other day. In this Remainder Theorem, we can say that if we do synthetic division with P(x) and a, then the remainder is always P(a). COOL. There's a proof at http://www.purplemath.com/modules/remaindr.htm that's really cool, btw.

Other polynomial things--

• The graphs of even-degreed polynomials always head for the same infinity while odds head towards opposites. However, the pattern skips over 0 because that's just what zero does. (Just kidding, it creates a horizontal line because anything to the zeroth degree is a constant)
• If a polynomial has an imaginary or even irrational root, then that root's conjugate is also a root. Also, a polynomial's degree is equal to its amount of roots (not including multiplicity).
• A polynomial to the nth degree has a graph with (n-1) curves.

So yeah, that's it for hoy.

Stay coolio...
John