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Update Unit 2: Sequences, Series, and Financial Applications.md
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**infinite series**: infinite series have **infinite** number of terms.
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- eg. $`1 + 2 + 3 + \cdots`$
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Terms in a sequence are numbered with subscripts: $~t_1, t_2, t_3, \cdots t_n`$ where $`t_n`$is the general or $`n^{th}`$ term.
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Terms in a sequence are numbered with subscripts: $`t_1, t_2, t_3, \cdots t_n`$ where $`t_n`$is the general or $`n^{th}`$ term.
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**Series**: A series is the sum of the terms of a sequence.
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@ -129,7 +129,7 @@ $`\large I = Prt`$
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- $`r`$ is the annual interest rate expressed as a decimal (the percent is $`1 - r`$)
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- $`t`$ is the time in years.
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- This interest is calculated from the original amount each time. (eg. if you had $$`100`$, and your interest is $`1\%`$, your interest will be a constant $$`1`$ each time.)
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- This interest is calculated from the original amount each time. (eg. if you had $100, and your interest is 1\%, your interest will be a constant $1 each time.)
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The total amount would be $`P + I`$.
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@ -168,3 +168,11 @@ Since it is basically the summation of a geometric sequence, we can apply the ge
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\large
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FV = \frac{R[(1+\frac{r}{n})^n - 1]}{\frac{r}{n}}
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```
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## Present Value Annuities
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The **Present Value** of an annuity is today's value of having equally spaced payments or withdrawals of money sometime in the future.
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```math
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\large
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PV = \frac{R[1 -(1+\frac{r}{n})^{-n}]}{\frac{r}{n}}
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```
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