Question

How can I prove that this sequence is increasing? http://dl.dropbox.com/u/6717478/Untitled.png

Answer 1

fancy mac screen shot...IR Jealous --- my book calls that the definition of increasing ..yay
and points out that is a monotic sequence...

Answer 2

Ok, that looks good, thanks.

Do you by any chance know how to determine whether it is bounded or not?

Answer 3

yes ... didn't review series in a while ...you might want to check

Answer 4

here's something similar : http://www.physicsforums.com/showthread.php?t=278723

Answer 5

I tried starting with that since (a_n) >=2 then
2(a_n) <= (a_n)^2 the worked forward from there to (a_n) <=(a_n+1)

which I think looks ok,

but as far as I can tell there is no upper bound. I know it clearly starts at 2, but then it jsut keeps getting bigger. Is there any way to determine this, or do I just tell from inspection?

Answer 6

I think that if you prove that it is monotic then if it has a limit or not will prove that it is bounded or and since a^2 has no limit it has no bound

that is how i am reading that chapter

Answer 7

well I'm not sure if it's monotonic, but part c of this question asks me to show that the limit of the sequence is 1 as n goes to infinity

Answer 8

here is the whole problem http://dl.dropbox.com/u/6717478/Untitled.png

Answer 9

monotic is just a fancy word for increasing or decreasing which is what mathg8 proved...

Answer 10

maybe post again with the new details....the notation in that problem is not like the stuff we are using sorry

Answer 11

Don't worry about it, thanks for your help though!

Answer 12

I've figured out the limit in part C, but I'm still unsure about the bound

Answer 13

A sequence an is bounded above if there is a number M such that:
an <= M for all n>=1

which looks like to me that if there is a limit M that an stays below then the sequence is bounded

Answer 14

another thing is that I thought this sequence was increasing, but it starts with 2 then goes to 1 as n goes to infinity. How can that happen.

I'm pretty sure these results are correct though since that's what part c is asking

Answer 15

what book are you using ?

Answer 16

That looks good but I don't have an equation for a_n only for a_n+1

Answer 17

yeah I already considered the derivative, but it won't work in this case

Answer 18

you have a_n ... look at my first attachment

Answer 19

my sequence doesn't have a unique entry for every n, each entry is dependent on the past entry. That method is for if they give you a function.

Answer 20

if the sequence is increasing and bounded it has a limit !

Answer 21

did you prove the sequence is bounded ?

Answer 22

well I found the limit, but the bound I wasn't so sure about

Answer 23

http://dl.dropbox.com/u/6717478/Untitled.png I've done parts a and c, but parts b and d are still giving me trouble

Answer 24

I'll work on it tomorrow ... when do you need it ?

Answer 25

by tomorrow, but even if you don't get it tonight, I would still like to understand it lol