Question

Easy Alg 2 Question :)

Answer 1

Do you now the sum for a geometric series?

Answer 2

No @xapproachesinfinity

Answer 3

okay! \[\sum_{n=0}^{\infty} a1r^n\]

Answer 4

that the sum of the geo series where a1 is the first term
r is the common ratio
now do that for this series!

Answer 5

@xapproachesinfinity okay so this crosses out A and B, so now I have C and D left

Answer 6

Correct!

Answer 7

you have to take the limit of that sum to determine if it is convergent and do the sum
of if it is divergent

Answer 8

@xapproachesinfinity how do you know the limit of the sum?

Answer 9

limit of the sum is sum of limit
so you only need to take the limit of the that expression a1r^n

Answer 10

@xapproachesinfinity so the answer is D, right?

Answer 11

why?

Answer 12

@xapproachesinfinity because it diverges when you take the sum of the limit?

Answer 13

Not really
what's the limit?

Answer 14

188?

Answer 15

how did you compute that! i have no idea xD
i think the limit is zero?

Answer 16

UGH I'm so confused lol

Answer 17

I thought you said to get the limit you solve a1r^n

Answer 18

and that would be 940(1/5)^1, so i got 188 lol

Answer 19

No

Answer 20

\(\large \it\color{maroon}{ \sum_{i}^{infinity}940(\frac{1}{5})^i }\)
\(\large \it\color{maroon}{ \lim_{i \rightarrow \infty}940(\frac{1}{5})^i}\)

Answer 21

that's the limit i told you to find!

Answer 22

So if the limit goes to infinite it can't have a number, therefore it's diverging?

Answer 23

@xapproachesinfinity

Answer 24

No what's the limit of that power thing?

Answer 25

it is not going to infinity!!

Answer 26

@xapproachesinfinity 0?

Answer 27

correct the limit is zero!
so the series is convergent
actually there a rule that says if r is less than 1 the series should convergent

Answer 28

okay, so the answer is C? :)

Answer 29

now you need to find the sum

Answer 30

well if it's convergent then i already know the answer can't be D, and since we eliminated A and B.... :)

Answer 31

well it is the answer C, but can we make sure!
i mean we are sure since there are no other options but
can we do it and find the sum

Answer 32

sure

Answer 33

well let's say for now the question is changed and asked to do the sum? what would you do

Answer 34

also after can you help me with one more?

Answer 35

you would substitute i into the power and solve it through

Answer 36

im not sure i have enough time

Answer 37

then raise the power by +1 and solve it through again, righ?

Answer 38

No, you need a formula to do this
using limits

Answer 39

it's really quick!! you just have to check my answer :)

Answer 40

what's the formula?

Answer 41

okay will see what we can do!

Answer 42

since this is geometric series there is a formula for Sn
Sn=a1(1-r^n)/1-r
Do you recognize this?

Answer 43

ohhhh yeah

Answer 44

also the next question is:

What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of -9? (5 points)

an = 3(-12)n - 1; all integers where n ≥ 1
an = 3(-12)n - 1; all integers where n ≥ 0
an = 3(-3)n - 1; all integers where n ≥ 1
an = 3(-3)n - 1; all integers where n ≥ 0


i know it can't be the first two, so would the answer be D?

Answer 45

well that should be easy
the first term is 3
the common ratio is -3
so the answer is c
the first term should be 3 so
all integers n greater than of equal 1

Answer 46

if it is d the meaning of common ratio will be last
check for n=0

Answer 47

you will dealing some other ratio

Answer 48

ok thanks i'll try

Answer 49

ok try to do the sum, i would like to see your result ^_^

Answer 50

how exactly do i do the sum -_-'

Answer 51

use the formula that i wrote above.
take the limit of that and see what it gives that should be your sum
will you already know it has to be 1175

Answer 52

well*

Answer 53

is this algebra 2 course! i thought series are in precalc or calc lass?

Answer 54

oh lol i was talking about the new problem -_-"

Answer 55

it's alg 2

Answer 56

mmm.. that's weird! anyways, did you do the sum?

Answer 57

yeah, it's 1175

Answer 58

okay! i think that answers your questions