\limsup_{n\to\infty} x_n := \lim_{N\to \infty}\sup\{x_k\,:\,k\geq N\}}

\liminf_{n\to\infty} x_n := \lim_{N\to \infty}\inf\{x_k\,:\,k\geq N\}}

La limite inférieure d'une suite:

n

sup

inf

M

m

n=

boite

Nmax = 687 (slider from -5 to 2000, step 1)
f(x) = 1 + (0.05 * (-1)^(x)) + (10 * sin(x^(2)) / (x / 2)^(0.3))
A = Point(xAxis)
N: (floor(x(A)), 0)
g = OrthogonalLine(N, xAxis)
endlist = Sequence(f(k), k, floor(x(N)), Nmax)
supremum = Max(endlist)
SUP: (floor(x(N)), supremum)
lignesup = Ray(SUP, SUP + (1, 0))
infimum = Min(endlist)
INF: (x(N), infimum)
ligneinf = Ray(INF, INF + (1, 0))
a = false
b = false
p, h, i, j, k = Polygon(INF, SUP, (Nmax, supremum), (Nmax, infimum))
len: x(N)
text1_2: "" + (LaTeX[len]) + ""
text4: "" + len + ""
l = Segment(SUP, N)
m = Segment(INF, N)
text6: "" + (LaTeX[len]) + ""
s = Sequence((n, f(n)), n, 1, Nmax)
c = false