Question

calculus II - is the sequence of an converges, then the limit as k--> infinity =0.
Corollary : if the limit of ak as k--> infinity is not equal to 0, then the summation of ak diverges.

This corollary is confusing because what if the limit of ak is equal to 0 wouldn't it by then converge?

I got confused

Answer 1

if the sequence*

Answer 2

the point is k approaches infinity, it never actually gets there so your value never actually gets to 0

Answer 3

yes, I know it'll diverege if it tends to infinity, but the prof said that if the limit of ak =0 then that doesn't mean that it converges. Isn't it confusing? because the first rule states that if the sequence converges , that means that the limit = 0.

lost lol

Answer 4

he said the contrapositive of the corollary is false, why?

Answer 5

that the*

Answer 6

well maybe he is saying that if the limit =0 then the corollary is false because the corollary is basically saying that 0 is an outlier (the dotted line, cant remmebr the correct name) and if it actually gets there then that isnt an outlier, rendering the first statement false?

Answer 7

lol, what are you trying to say?

Answer 8

im saying if the first thing claims that you cant be at 0 and the second thing says that you are at 0 then the first thing is lieing

Answer 9

but the first thing says that it is at 0

Answer 10

an the first rule is correct

Answer 11

and*

Answer 12

no, the first part says you get really close to 0, you never actually get there

Answer 13

yes I know, it'll "approach" zero, still this says that it'll converge

Answer 14

yeah, at infinity... which you cant get to, meaning you cant get to 0. and if your at 0 then your limit reached infinity. thats pretty intense if you reach an unreachable number

Answer 15

which part are you talking abt lol, the first rule? or the corollary?

Answer 16

you're running in circles >_<

Answer 17

exactly, the circles is on purpose. the second statement renders the first one false.

Answer 18

convergence means that the sequence will end with a finite number while divergence means that the sequence will reach infinity or will have an alternating endless value.

Answer 19

be direct , please

Answer 20

I've been in enough circles already x_x with my prof

Answer 21

how does this corollary work? if it's not equal to 0, then I agree, it diverges, but what if it actually is = 0?

Answer 22

wouldn't that mean that it'll converge?

Answer 23

I was told that it's false, it won't converge , we'll actually don't know what it will do, but WHY?! LOL

Answer 24

what difference does it make?

Answer 25

i guess im confused by the original statement. but if you have a number lim approaching infinity = anything. it never reaches that "anything" so i'd say it does NOT converge

Answer 26

see what I mean? I am too, that's why I have asked LOL

Answer 27

confused too, starlet

Answer 28

by the way, how are you?

Answer 29

great thx :), yes I am confused :(

Answer 30

wait a sec, angoo!

Answer 31

:) who else would it be if not me :)

Answer 32

have you seen the new groups?

Answer 33

happy birthday ^_^! no one else calls me starlet but you

Answer 34

yep :)

Answer 35

:) nice, well, it is good that OpenStudy is improving... anyway, got my exams to university on the 12th, thats like i have 3 days to study :)

Answer 36

no 2 days to review and one day to relax

Answer 37

oh, and have you heard of a website called khan academy

Answer 38

nope

Answer 39

khan academy is boss. fact.

Answer 40

so mimi, whats up? oh, and you can see the intro vid at http://www.khanacademy.org/

Answer 41

dunno, never heard about it, but will do , later on when I'm done with my midterms

Answer 42

lol, nothing but midterms are up starting on Sunday, I haven't been here for 2 days now, you?

Answer 43

I was surprised by the number of videos and topics ONE guy made it is just crazy
http://www.khanacademy.org/#browse
have a quick look at the list

Answer 44

I did + faved it to go through it later

Answer 45

ok, anyway, have any plans for today?

Answer 46

yeah, one of them is to wish you a great HAPPY BIRTHDAY

Answer 47

ok, thanks =D you are the first person that did it =D

Answer 48

I know =P np :) and the other plans is to get ready and look like a princess for my sister's engagement part tonight ^^"

Answer 49

which is the thing that I'm not looking forward to ._.

Answer 50

yey! nice, engagement..... so are you going to post some pics of yourself as a princess online?

Answer 51

no >_>

Answer 52

LOL, I knew it

Answer 53

I don't like strangers touching my hair or anything else!

Answer 54

so how is Dubai?

Answer 55

been windy from time to time, but good

Answer 56

how's finland?

Answer 57

LOL the snow is starting to melt

Answer 58

aww :(

Answer 59

which I am really happy about

Answer 60

I need summer

Answer 61

I love summer, but would love to play with the snow lol

Answer 62

well, some time once you finish your studies you will go to a winter country..
am I right?

Answer 63

maybe, I do love the country though :)

Answer 64

I mean, not to live but to visit :)

Answer 65

far away from the people where peace and quite can be attained :) , that's one of my dreams. Is to live in simple small house, with a beautiful garden, waking up in the morning for walks and etc.

Answer 66

oh, yeah lol I guess

Answer 67

well, in that case it might be easyer to live in a warm country.... anyway it is nice to travel

Answer 68

yes it is ~

Answer 69

Enough about me, what about your plans?

Answer 70

my plans are to practice derivation, differential equations, some pre calculus stuff, maype some physics.... well basically anything that might help me in exams :)

Answer 71

only for 2 days, and the last day is to do something fun, right?

Answer 72

no... last day I will stdy like mad.. read calculus, STEP III, and stuff like that, I need to fill my brain with info

Answer 73

no no and no

Answer 74

do you want to mess up?

Answer 75

I dont want to mess up, I wanna pass...

Answer 76

then have fun the last day!

Answer 77

why? how will that help me pass? I just don see it.

Answer 78

relax :)

Answer 79

it's like you are releasing all the stress and pressure out just before the test. This will help you to get a good shut eye and great energy in the morning

Answer 80

ok, I will only study half day... and the rest I will spend relaxing

Answer 81

no

Answer 82

you'll only be getting yourself nervous.

Answer 83

I am already nervous, alot :(

Answer 84

on this my depends my future

Answer 85

see

Answer 86

listen, did you study?

Answer 87

what do you mean?

Answer 88

did you study? Yes/No?

Answer 89

today?

Answer 90

I just woke up

Answer 91

no, in general

Answer 92

yeah, I studied, but there are still somethings I need to revise.
But I am just afraid I can do worse than other 40 guys. Because there are alot of applicants, like 300 and out of those 300, 40 best will be taken.

Answer 93

Do you really believe that you won't be one of these 40 guys?

Answer 94

well, I dont know, it is imposible to know the future, those 300 applicants might be studing really hard, and might be better prepared. Of course, anything can happen. I just hope I get in, because if I don't, I will have to quickly figure out what to do :)

Answer 95

do you want to pass?

Answer 96

yeah, heaven yeah

Answer 97

then you are going to be one of those 40 guys. :) Put that in mind. A person that knows what he/she wants, and is clear about it, will reach what he/she wants :) and you will

Answer 98

all you've got to do, is have a good night sleep, wake up fresh in the morning, heavy breakfast and ace that exam!