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Update Unit 2: Sequences, Series, and Financial Applications.md

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James Su 2020-03-06 19:44:25 +00:00
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**infinite series**: infinite series have **infinite** number of terms.
- eg. $`1 + 2 + 3 + \cdots`$
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.
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.
**Series**: A series is the sum of the terms of a sequence.
@ -129,7 +129,7 @@ $`\large I = Prt`$
- $`r`$ is the annual interest rate expressed as a decimal (the percent is $`1 - r`$)
- $`t`$ is the time in years.
- 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.)
- 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.)
The total amount would be $`P + I`$.
@ -167,4 +167,12 @@ Since it is basically the summation of a geometric sequence, we can apply the ge
```math
\large
FV = \frac{R[(1+\frac{r}{n})^n - 1]}{\frac{r}{n}}
```
## Present Value Annuities
The **Present Value** of an annuity is today's value of having equally spaced payments or withdrawals of money sometime in the future.
```math
\large
PV = \frac{R[1 -(1+\frac{r}{n})^{-n}]}{\frac{r}{n}}
```