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cards-deck: default_obsidian
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#math/calculus 

# definition of series
#card/reverse 
The sum of a [[sequence]]. Use the $\Sigma_{n=1}^\infty$ notation.
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# partial sum
It's a series that converges to a value. So, you're doing *part* of the sum at a time.

# algebraic vs geometric
Algebraic series ::: the function uses n in the function as a normal coefficient. ^1652972454834

# Geometric series
#card/reverse
the function in the series uses n as an exponent. Thus, the growth is big very cool.
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$a$ is the constant, $r$ is rate

Formula for value at any n: ==$S_n=\frac{a(1-r^{n})}{1-r}$==
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Formula for value at infinity(a is the start): ==$S_n=\frac{a}{1-r}$==
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## nice little formula
$\Sigma_{n=1}x^{n}$ and $|x|<1$
$a=x$
$= \frac{x}{1-x}$
if: 
$n=0$
$a=1$
$= \frac{1}{1-x}$

# sum properties
- $\Sigma c\cdot a_{n} = c \cdot \Sigma a_{n}$
- $\Sigma (a_{n}+b_{n}) = \Sigma a_{n}+ \Sigma b_n$
- $\Sigma (a_{n}-b_{n}) = \Sigma a_{n} - \Sigma b_n$