concepts about series

[shahar]

What is the deference between the term:
(a) bounded sequence at the value a
to the term:
(b) The limit of the sequence is a.

 

[pka]

What is the deference between the term:
(a) bounded sequence at the value a
to the term:
(b) The limit of the sequence is a.

In this reply [imath]n\in\mathbb{N}^+[/imath]
Consider [imath]s_n=(-1)^n+\frac{1}{n}~\&~t_n=-1+\frac{1}{n}[/imath].
Both of those sequences are bounded but only one has a limit.

[imath][/imath]

 

[shahar]

In this reply [imath]n\in\mathbb{N}^+[/imath]
Consider [imath]s_n=(-1)^n+\frac{1}{n}~\&~t_n=-1+\frac{1}{n}[/imath].
Both of those sequences are bounded but only one has a limit.

[imath][/imath]

The bound of the sequences is negative number like -1 and etc.
What is the limit? How I find it?

 

[pka]

The bound of the sequences is negative number like -1 and etc.
What is the limit? How I find it?

Can you answer each of these?
[imath]{s_3} = \boxed{|\;\;\;\;\;\;}\quad {s_{100}} = \boxed{|\;\;\;\;\;\;}\quad {s_{1001}} = \boxed{|\;\;\;\;\;\;}[/imath]
[imath]{t_3} = \boxed{|\;\;\;\;\;\;}\quad {t_{100}} = \boxed{|\;\;\;\;\;\;}\quad {t_{1001}} = \boxed{|\;\;\;\;\;\;}[/imath]
If not then you best ask yourself: "how ready am I for these problems?"

 

[shahar]

[imath]{s_3} = \boxed{|\;\;\;\;\;\;}\quad {s_{100}} = \boxed{|\;\;\;\;\;\;}\quad {s_{1001}} = \boxed{|\;\;\;\;\;\;}[/imath]
[imath]{t_3} = \boxed{|\;\;\;\;\;\;}\quad {t_{100}} = \boxed{|\;\;\;\;\;\;}\quad {t_{1001}} = \boxed{|\;\;\;\;\;\;}[/imath]
If not then you best ask yourself: "how ready am I for these problems?"

By your method, the second has a limit because it decrease and decrease = sequence t.

 

[shahar]

Can you give an example to unbounded sequences...