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?
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2
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3$\begingroup$ Remove "Integer" $\endgroup$– ZaMoCCommented Nov 5, 2018 at 20:02
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1$\begingroup$ Moreover, DiscreteLimit[L[k], k -> Infinity] is unevaluated too. $\endgroup$– user64494Commented Nov 5, 2018 at 20:11
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1 Answer
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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_] :=
Piecewise[{{(k/(k - 1)), Element[k, Integers]}, {Indeterminate,
True}}]
DiscreteLimit[lL[k], k -> Infinity]
(* Out[113]= 1 *)
answered Nov 5, 2018 at 20:35