- #1

- 19

- 0

I think use [itex]\exists{\epsilon>0}\forall{N\in\mathbb{N}}\exists{n\geq N}:|a_n-\ell|\geq\epsilon[/itex]

How i can continue?

- Thread starter solakis
- Start date

- #1

- 19

- 0

I think use [itex]\exists{\epsilon>0}\forall{N\in\mathbb{N}}\exists{n\geq N}:|a_n-\ell|\geq\epsilon[/itex]

How i can continue?

- #2

- 33

- 0

Try showing that it's not a cauchy sequence instead and then just say "therefore it is not convergent."

Last edited:

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

Alternatively, note that [itex]a_n= 1[/itex] for n even, [itex]a_n= 3[/itex] for n odd. For any l, there exist arbitarily large n such that [itex]|a_n- l|> 1[/itex], half the distance between 1 and 3.

- #4

- 19

- 0

So which do you think should be the value of ε>ο ??

- #5

Deveno

Science Advisor

- 906

- 6

HallsofIvy just told you what epsilon to use, half the value of the difference of the two possible values any term of the sequence can have.So which do you think should be the value of ε>ο ??

- Replies
- 6

- Views
- 3K

- Replies
- 7

- Views
- 878

- Replies
- 7

- Views
- 886

- Replies
- 12

- Views
- 520

- Replies
- 2

- Views
- 867

- Replies
- 4

- Views
- 3K

- Replies
- 8

- Views
- 722

- Replies
- 4

- Views
- 1K

- Replies
- 2

- Views
- 2K

- Replies
- 2

- Views
- 855