CHEWY'S AND GABY'S SCRIBE POST

Hi! It’s me Chewy and Gaby, today is our turn to make the scribe, and this was today’s POD.

POD 6/1:

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?

First list the 1st few terms:

2000, 1600, 1280, 1024…

How did we get those terms?
Well we multiplied 2000(4/5) =1600, 1600(4/5) =1280, etc…

So we use the Geometric Series formula to solve this problem.

*REMEMBER THAT THE DAY SHE WAS BORN IS NOT A BIRTHDAY DAY, SO WE START COUNTING FROM 19.

Formula: Sn = T1 (1-r^n)/ (1-r)
T1=2000 r= 4/5
S19= 2000(1-4/5^19)/ (1-4/5)
That equals approximately,
$9,855.88.

Now, assume that Frieda and her parents live forever. How much money will Frieda collect?

REMEMBER THIS IS AN INFINITE GEOMETRIC SERIES AND 4/5 IS THE RATE, AND IT IS LESS THAN 1.
So we use Sn= T1/1-r
Sn= 2000/1-4/5
Sn= $10,000

In this problem we are looking for Sn, so we just have to plug in for T1 and r.

Now, assume that Frieda’s parents gave her 5/4 as much every year for 18 years? Forever?

Answer for 5/4 as much every year for 18 years.
Procedure: Just plug in T1, r, and n.

S19= (1-5/4^19)/(1-5/4)
S19= $ 547.111.51

Answer for Forever:
Sinceﺍit’s greater that 1, then limSn = DNE and ∞, because it’s always getting a bigger number. lrl>1
After all that practice in series problems we continued on our last topic, Infinite Geometric Series.

Today we started learning how to use this formula:

LimSn=limT1 1-r^n/1-r
nà∞ nà∞

lrl>1

So 1-r^n (above) equals -∞

So the formula will reduce to Sn=T1 1- ∞/1-r= T1 +/- ∞/small number Sn= DNE

lrl<1>

So the formula will reduce to Sn=T1 1-0/1-r = T1 1/1-r = T1/1-r



VERY IMPORTANT!!!!!

WE HAVE A QUIZ ON FRIDAY ABOUT: INFINITE SERIES, LIMITS, AND SUMMATION NOTATION.

SUMMATION NOTATION IS THE TOPIC THAT WE ARE GOING TO LEARN ON MONDAY.

REMEMBER TO START STUDYING FOR THE FINAAAAAL!

Practice:

Find the sum of the infinite series.

3+2.4+1.92+1.536

1st find r; 2.4/3=.8, 1.92/2.4=.8
R=.8

Sn= T1/1-r
T1=3, r= .8

Sn= 3/1-.8
Sn=15

TASK:
Make up your own problem:

Choose some real number for T1
Choose some r such that lrl<>Find S10 and S∞
Exchange just the terms
Solve each others problem
Check with the author

Gaby’s Group Problem:

T1=12, r=2/3

12+8+5.33+3.555…

Sn=T1 (1-r^n)/(1-r)
S10= 12(1-(2/3) ^10)/ (1-2/3)
S10= approximates to 11.33

S∞=12/1-2/3
S∞= 36.0

WELL THAT’S IT FOR TODAY…WE HOPE THAT OUR SCRIBE HELPS YOU GUYS TO UNDERSTAND THIS TOPIC BETTER!!
GOOD LUCK ON FINALS!!

WE CHOOSE BEE AND DC FOR THE NEXT SCRIBE.

CHEWY AND GABY!