Question

I am totally lost on proving limits of sequences. I need some help.

Answer 1

1. I don't understand what exactly I'm supposed to be doing. Finding the epsilon?
2. I'm confused that there seem to be so many methods.
3. Is it sufficient to just always use the ceing of 1/epsilon?

Answer 2

*ceiling

Answer 3

yo

Answer 4

not sure what you are doing. what is the sequence?

Answer 5

for example prove n+1/(3n-1) converges to 1/3

Answer 6

need to have some n>N=something with epsilon

Answer 7

i do this thing...take absolute value of the function minus the limit and make it less than epsilon

Answer 8

http://www.cramster.com/mathematical-proofs-2nd-edition-chapter-12-problem-31AE-1453264

Answer 9

Ok, I understand I'm supposed to show that at some point that the value of the function will always be bounded by some epsilon plus and minus the limit

Answer 10

ah ok and you want to do it for real. in other words you want to say for any
\[\epsilon > 0 \exists n \]
sorry door

Answer 11

my final is tomorrow morning at 8. i'm so screwed on this

Answer 12

your job is to find the N that works for epsilon, that is given epsilon > 0 find the N (a function of epsilon) such that if n > N ,
\[|a_n-L|<\epsilon\]

Answer 13

so what you do is work backwards. you want to say that the limit is
\[\frac{1}{3}\] right?

Answer 14

yeah

Answer 15

so first we do a little algebra

Answer 16

\[|\frac{n+1}{3n-1}-\frac{1}{3}|<\epsilon\]

Answer 17

So, what I'm supposed to first find the epsilon, then use that as the ceiling?

Answer 18

no no you do not find the epsilon, you find the N

Answer 19

it is early, what is that inside thing?

Answer 20

i think it is
\[|\frac{4}{9n-3}|<\epsilon \]right?

Answer 21

yeah

Answer 22

ok so that is what we have, and we want to say that if n is bigger than some N we know this is true. so a bit more algebra is all is needed

Answer 23

so N > 4+3epsilon/9epsilon

Answer 24

so that's my ceiling value for N?

Answer 25

so that's basically saying, as long as n is greate than this value, this will converge to 1/3

Answer 26

hold on a second