I'm moving tomorrow, and I'm not sure I'll have internet there so I'm trying to download as many Calculus and Linear Algebra videos by Khan Academy as I can. If you haven't read about Khan Academy or seen Khan's videos already, and you want to understand math, biology, and even chemistry, then go check him out on Youtube.
I read a little today about the difference between a sequence and a series. A sequence is a list of numbers with or without a relationship between the numbers, and a series is the sum of all the numbers or terms in a sequence. There are two main types of sequences: there are algebraic sequences and there are geometric sequences. The difference between geometric and algebraic sequences is in the difference (pun intended).
In an algebraic sequence, you have a list of numbers in an order, each having a common difference. Common difference means you can subtract any term in the list with the term after or before it and get the same difference no matter what term you choose. In geometric sequences, there is a common ratio. Instead of getting the difference, the ratio is the same for any term before or after whatever term you choose in the list.
I hope to learn in more detail why geometric sequences, in particular, are important to Calculus. I think that the answer lies within the integral being an infinite sum of a product. I'm not sure my choice of words is correct but I think I'm onto something.
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