Tuesday, June 3, 2008

Introducing Series

The first thing we did in class today is answer some simple questions. Pretty straight forward, should be easy to do. Even if you weren't in class yesterday. Noo excuses, 'cuz I wasn't in class yesterday.

We also graphed the function 'y = [square root] x', which looks like half a sideways parabola.

Next, we learned about 'young Gauss', who was a pretty clever seven-year-old. His teacher told the class one day to add up all the numbers from 1 to 100. Instead of writing it all out and adding it, he found a pattern.

When the numbers are laid out like above, their sums equal 101. There should be a hundred 101's, hence the reason we multiply 100 and 101. We divide it because you added one hundred twice. That's what Karl Gauss figured out. If you want to know the details, you can go ahead and visit this link: http://www.sigmaxi.org/amscionline/gauss-snippets.html

Using the same idea as above, we found the formula for an arithmetic series.
Sn = (n/2)[2a+(n-1)d]

A series is the sum of numbers in a sequence to a particular term in a sequence (definition can be found on blog). You can't have a series if you don't have a sequence first, or else, what are you adding?

We also found the formula for a geometric series.
Sn = [a(1-r^n)]/(1-r)

Lastly, we touched a little bit on 'Sigma', which is located on the second-last slide (8).

Mmm, yeah, that's it. I'm tired now, I'm sorry. Hahaha, next scribe is Joseph, since he asked.. again.

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