# How to evaluate limit of a user-defined function

Limit[(k/(k - 1)), k -> Infinity]


Gives correctly:

1


But,

L[k_Integer] := (k/(k - 1))
Limit[L[k], k -> Infinity]


leaves the limit unevaluated.

How can I tell Mathematica to evaluate this limit?

• Remove "Integer" – J42161217 Nov 5 '18 at 20:02
• Moreover, DiscreteLimit[L[k], k -> Infinity] is unevaluated too. – user64494 Nov 5 '18 at 20:11

The input restriction means it is basically not amenable to analysis by Limit or even DiscreteLimit. If instead it is defined piecewise then the sequence limit can be found.
lL[k_] :=