Ok, quick apology to those in both classes. Note to self, make sure your notes are in order before teaching.
Recap of the problem.
Taking 500mg of acetaminophen every 4 hours and your body gets rid of 59% every 4 hours(leaving 41%). How much acetaminophen is in your body after you take the n-th dose.

Take a look at the sequence first:(in other words what is happening to the original amount that you took)
500, 205, 84.05, 34.46…

a) Write a recursive formula for `a_n`
so we have a common ratio of .41 and can write a common ratio as `r=(a_n)/(a_(n-1))`
Solve for `a_n` and you have your recursion formula. `a_n = .41(a_(n-1))`

b) Show that `a_n` can be viewed as a geometric series.
ans: if you show that the sequence has a common ratio for the given terms, then you can represent it in a geometric series (i.e. add them up)
`S_n`=500 + 205 + 84.05 + … `t_n`
c ) Find `S_18`

Now we use the partial sums formula `S_n=(1-r^n)/(1-r)`, Where:

n=18 (This is the number of terms your adding in the sum)
r=.41 (this is your common ratio)

`S_18`=847.4575363
note: this is the sum of the 1st 18 terms(500 + 205 + 84.05 + 34.46+…+`t_18`)
d)
`S_19`= 847.4575899
`S_21`=847.4576209

Notice that we are approaching a limit. Why does it approach a limit?