Question

PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I WILL AWARD MEDAL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


Part 1: In complete sentences, explain the necessary steps required to find the geometric partial sum the sum (Look at equation below). Be sure to give your final answer in your explanation. (3 points)

Part 2: Is this partial sum divergent or convergent in nature? Explain your answer.

Answer 1

\[\sum_{i=1}^{5}3(0.1)^(i-2)\]

Answer 2

@CarlosGP @primeralph @Loser66

Answer 3

Now the formula is a bt diferent. If "r" is the common ratio, you have:\[S_N=\sum_{n=1}^{N}a_n=\frac{ a_1-r·a_N }{ 1-r }\]

Answer 4

in your case, r=0.2
Find a1 and aN

Answer 5

OK one sec please.

Answer 6

How do I find the common ration if I am not given any terms to add and divide to reach the common ratio.

Answer 7

Sorry, the common ratio in your case is 0.1. You find it in this way:

\[a_{i}=3·(0.1)^{(i-2)}\]
\[a_{i+1}=3·(0.1)^{(i+1-2)}=3·(0.1)^{(i-1)}\]\[r=\frac{ a_{i+1} }{ a_i}=\frac{ 3·0.1^{i-1} }{ 3·0.1^{i-2} }=0.1\]

Answer 8

got it?

Answer 9

OK.

Answer 10

now apply the formula

Answer 11

a1=? and a5=?

Answer 12

I do not know because I am not give a1

Answer 13

But you have: ai, just replace the "i" with "1"

Answer 14

Oh ok

Answer 15

Dont you get:\[a_1=3·0.1^{(1-2)}=3/0.1=30\]

Answer 16

It is 1.003

Answer 17

see my calcullation and try again

Answer 18

ok

Answer 19

now repeat for n=5

Answer 20

or replace i with 5

Answer 21

dont you get \[a_5=3·0.1^{5-2}=0.003\]

Answer 22

no

Answer 23

what do you get?

Answer 24

Oh yes that is what I got

Answer 25

excellent, now apply the formula, you have all that you need:\[S_n=\frac{30- 0.003\times 0.1 }{ 1-0.1 }=????\]

Answer 26

It is 33.333

Answer 27

Awesome!

Answer 28

Have you caught the whole process?

Answer 29

Yes but I am not sure how to sum it up how my teacher wants it written for part 1 and part 2

Answer 30

We have done part1. All the process is explained above
For part 2, whenever the module of the common ratio is <1 the sum is convergent

Answer 31

Ok. If it is not to much can you sum up all we did in one post PLESASE

Answer 32

I would love to but I have to go. I think the whole process is perfectly developed throughout all the posts. This is a good exercise for you to summarize anyway!

Answer 33

OK can I sum it up and you tell me if it is right PLEASE

Answer 34

all right but not today. i gotta go and will have a look at it tomorrow (Spain´s time). send it to me in a message

Answer 35

OK. Bye

Answer 36

bye