# There is a way to evaluate the limit superior of a sequence?

Is there a way to evaluate the limit superior of a sequence? I didn't find any information about this in the documentation center.

The limit superior of a sequence $(x_n)$ is defined as

$$\limsup x_n=\lim_{n\to\infty}\sup\{x_k:k\ge n\}=\inf\{\sup\{x_k:k\ge n\}:n\in\Bbb N\}$$

• Theoretically, Assuming[n ∈ Integers, Limit[MaxValue[{x[k], k >= n}, k, Integers], n -> Infinity]], but practically there are probably limitations depending on x. – Michael E2 Nov 1 '16 at 11:43

Max[Limit[expr, n -> Infinity]]

• I think I should say that because the limit of a sequence from Mathematica (If it works.) probably gives an interval.(I guess) Then you just take the max value of the interval. ex. Limit[(-1)^n (1 + 1/n), n -> Infinity] gives (*E^(2 I Interval[{0, \[Pi]}])*) – tablecircle Nov 2 '16 at 8:36