Question

Consider the series
−3/4+9/16−27/64+81/256+⋯
Determine whether the series converges, and if it converges, determine its value.

Enter the value if the series converges, or enter DNE if it diverges:

i have no idea what this means...the sequence is (-3/4)^n...i tried entering the 5th entry...i tried entering (-3/4)...i tried entering (-3/4)^n...tried even DNE...but all wrong...i have no idea what it means by "determine it's value"

Answer 1

does this look familar?
\[\sum_{n=1}^{\infty}(-1)^n*3/4^n\]

Answer 2

no

Answer 3

i know that's the symbol for sum of something

Answer 4

what course are you in?

Answer 5

calc 2

i think i missed this lecture

Answer 6

math 214?

Answer 7

or something like that?

Answer 8

mat 266. calc for engineers at asu

Answer 9

okay...ummm do you know what the name of the section it is under is? Cause there are a couple different strategies to doing it and I don't want to give you one you can't use

Answer 10

series and sequences.

Answer 11

the subsection I mean

Answer 12

that's what it says on my syllabus. he doesn't use a book. it just says "series and sequences"

Answer 13

..o boy ummm well. That would be why you are having trouble if you missed the lecture. They are completely different limits than normal

Answer 14

i'm trying to watch video's on khan academy but there are so many in the sequences and series section.

Answer 15

Sorry but I haven't taken that course personally and I'd be afraid of showing you something different than what you are suppose to do.

Answer 16

as long as i get the right answer, i doubt he cares. i can't follow when he's teaching anyway. everything i have learned so far has been from khan academy. he doesn't explain himself very well.

Answer 17

can someone please just show me something???? i am so confused and ready to cry. please help!!! the test is Wednesday. please!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 18

What was the previous topic you did?

Answer 19

i took the limits of series.

Answer 20

Did you check your book how to do this?

Answer 21

i don't have a book....hence the problem.

Answer 22

This is calculus 3 actually.

Answer 23

You have to find the sum

Answer 24

How do you not know summation and you're in calc 2..?

Answer 25

because he just taught this to us and i missed the lecture....

Answer 26

thank you for being condescending though....

Answer 27

Just saying how do you not know sigma notation and you're in calc 2 :\.

Answer 28

i know that sigma thing is summation. the rest of it i don't know

Answer 29

i already said that if you scroll up...i said i know that E thing means summation. but i don't know how to set up the rest of the problem

Answer 30

I haven't done this before but I am looking at my book.

Answer 31

and i didn't know that was what we were supposed to do here....that's why the question asked "what does determine it's value" mean

value of what? next value in series? sequence value? that's why i'm asking....

Answer 32

Do you remember the topic or chapter name of this or the one right before, so I know where exactly to look.

Answer 33

we don't have a book, but it's series and sequences

Answer 34

i've said that 3 times now

Answer 35

Determine whether the series converges, and if it converges, determine its value

Answer 36

How do you not understand that...it's asking you if the series converges and if it does determine its value...

Answer 37

BECAUSE I DON'T UNDERSTAND THAT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 38

flutter it if no one is willing to fluttering help me without judging me and belittling me than i will just fluttering fail. flutter you,

Answer 39

wait sec

Answer 40

whoa this sequence converges....

Answer 41

I know that 100% for sure

Answer 42

by find the value it means find the value of all the terms summed together if you were to continue that summation on to n=infinity

Answer 43

ok... so here is something, the series is geometric

the common ratio is -3/4

since its -1 < -3/4 < 1

the series converges and has a limiting sum

so then you can use the limiting sum of a geometric series

\[s_{\infty} = \frac{a}{1 - r}\]

r is the common ratio -3/4 and a is the 1st term -3/4

substitute and you'll find what it converges to

Answer 44

iambatman, how about you try to be a little nicer to people instead of being a condescending donkey "How do you not know this" and reducing someone to tears making them think they are stupid. i am bawling my eyes out because apparently, i'm stupid and supposed to already know this. i hope you're proud of yourself

Answer 45

is a really simple solution.... just don't over think things

Answer 46

Mhm, if you don't get it that's fine it's calculus it's suppose to be tough, just don't blame me for you problems. You should really buy the textbook, it's very useful, I suggest James Stewart 7th edition.

Answer 47

so it's .75/(1+.75)

Answer 48

well almost try (-3/4)/(7/4)

Answer 49

THERE IS NO TEXTBOOK FOR THIS CLASS! HE DOESN'T USE ONE!!!!!!!!!!!! and i'm blaming you for your choice of words. and i can't buy the textbook when my bank account is sitting at .30 cents

Answer 50

use fractions as they will give an exact value... no decimals

Answer 51

@campbell_st o god I forgot that works for alternating series too jeeze

Answer 52

thank you, campbell st. that was the right answer.