Limit of a sequence

[Gerino]

I am looking for an algorithm, function or something else, that would
find limit of a sequence, while given formula i.e. a[n] = n/(n+1) (or
any other). Is such thing even possible? I can calculate any number of
points, a[1], a[2]...a[n], but is there any method to find limit of a
sequence in general case?

 

[Kai-Uwe Bux]

I am looking for an algorithm, function or something else, that would
find limit of a sequence, while given formula i.e. a[n] = n/(n+1) (or
any other). Is such thing even possible? I can calculate any number of
points, a[1], a[2]...a[n], but is there any method to find limit of a
sequence in general case?

No.


Best

Kai-Uwe Bux

 

[Markus Schoder]

I am looking for an algorithm, function or something else, that would
find limit of a sequence, while given formula i.e. a[n] = n/(n+1) (or
any other). Is such thing even possible? I can calculate any number of
points, a[1], a[2]...a[n], but is there any method to find limit of a
sequence in general case?

No.

True. But just to be clear it is not only that nobody has found such a
method yet. It is provable that no such method exists at all for the
general case.

 

[Gerino]

Thanks for answers. And is there any method to get an approximation of
this limit?

 

[Kai-Uwe Bux]

Thanks for answers. And is there any method to get an approximation of
this limit?

a) If I am not mistaken, there is not even a method to decide whether a
sequence has a limit.

b) Computer algebra systems employ a lot of heuristics to find answers in
many cases.

c) This is off-topic in this group anyway and you may find better answers in
comp.programming or some group in the sci.math or sci.logic hierarchies.


Best

Kai-Uwe Bux