Scribe June 1

Well, first of all I want to wish good luck to all the students running for an officer position at STUCO. This is not relevant to Pre-Calc, but still, our classmates need to know we support them!

As always, I was late to class and missed the POD. However, Eli copy it for me. So please if there's any mistake tell me!!!.. jajajaja
POD
When Frieda was born her parents gave her 2000 dollars. On each subsequent birthday, they gave her 4/5 of the amount they gave her the year before. On Frieda's 18th birthday, what is the total amount since birth that Frieda would have received?
-So, first of all this is a geometric series! It ask for the TOTAL AMOUNT, not how much will she get on the 18th birthday.
The rate is = 4/5
t1 is = 2000
and we need to find S18
STEPS
1) Get the second and third term to see if the final answer is correct.
2000(4/5)=1600
2000+1600..+.......+.........
2) To get our final answer we use the formula Sn= t1((1-r^n)/(1-r))
So, PLUG IN the given numbers!
S18=2000((1-(4/5)^19)/(1-(4/5))
*WHY 19??? well, there are 18 birthdays + the actual day she was born so it's the 19th number!
3) Get the answer, which is aprox $9855.88

Now, changing the question a little bit:
Assume that Frieda and her parents live forever (inmortals, yeah right), how much money will Frieda collects?
If you remember, on Wednesday, Mr. Rumidog gave us a formula to solve this type of problems. The formula is S=(t1/(1-r)).
So again, just PLUG IN!
S=(2000/(1-(4/5)))
S=$10,000
Which means that our limit is $10,000, when n goes to infinite.

Now, change the problem again…
What if Frieda’s parents gave her (5/4) as much as every year for 18 years? Forever?
-18th birthday:
S18=2000((1-(5/4)^19)/(1-(5/4))
S18= $547,111.51
-Forever:
S=2000/(1-(5/4))
S= -$8,000
*WRONGGGGGG!!!!!!!!!!!!!!!!!!
The “Sum of an Infinite Geometric Series” states that: If r≥ 1, tn ≠ 0. This means that the equation we just use can only be used if r is ≤ 1. *5/4 is ≥ 1*
The correct way to answer the question is the following:
Sn=t1((1-(r)^n)/(1-r))
So, how she is earning for ever, we may say that r^n is = .
Answer: DNE!
*Isa then stated that if the rate is greater than 1 then the answer will be INFINITE.

Finally, after the LONGEST POD EVER, Mr. Rumidog recommended to visit B.Bustillo’s everything site.

HEY! We are also going to have a QUIZ on FRIDAY!!!!
The topics on the quiz will be:
· Limits
· Infinite series
· And a new topic that he is going to teach on Monday called “The Sum of an Infinite Series”
To practice for the quiz there is HOMEWORK! Pg: 503 #23-31 odd and 35


So, going back to the Achilles’ problem, we may now use our formula.
So the series will be 10+1+(1/10)+(1/100)
Formula: S=(t1/(1-r))
r=1/10
t1=10
So, PLUG THEM IN!
S=(10/(1-(1/10)))
S=(10/(9/10))S=100/9S= 11 1/9 m

Now, a practice problem:
Find the sum of the following series:
3+2.4+1.92+1.536+…
r= 2.4/3 = .8
Sn=(3/(1-.8)) = 15
Dark Angel said: The rate is less than the absolute value of 1!!

New task:Create your own problem!!1. Choose some real # for t1, NOT 02. Choose some R such that r<1 and r≠03. List the first 4 terms of your series4. Find S10 and S 5. Exchange just the terms6. Solve each others problems7. Check with the author

So, Dark Angel and I did the task together… this is our problem:1. T1= 112. R= .13. 1+1.1+.114. S10= 11((1-.1^10)/(1-.1)) =12.2
S =(11/1.01) = 12.2

After solving these problems, Kris asked about Infinite Arithmetic Series.
The Arithmetic Infinite Series consists on adding an infinite # of numbers. (Sn= t1+t2+t3+…+tn)
A practice problem:
t1= 5d= 8(5+13+21+…)
or
d= -8
(5+ (-3) +(-11) +(-19)…)
Sequence: Start at some number (t1) and repeatedly add some # d (not 0).
D>0, t1 increases without bound. (Sn=? = ) DNE
D<0, t1 decreases without bound (Sn=? = - ) DNE
Infinite arithmetic series cannot have a finite sum.

Next Scribe:
Daniel + Jorge = Monday!!!