Proof without words: Limit of a recursive sequence

3/1 (2005), 121–122
Proof without words:
Limit of a recursive sequence
Pilar Abreu, Esther Guerra and Ángel Plaza
x0 > 0 &
xn+1 =
xn
2
+
2
xn
−→
lim xn = 2
n→∞
y = x
y = x/2+2/x
2
x0
2 x3
x2
x1
Figure 1. 0 < x0 < 2
c 2005 by University of Debrecen
Copyright 122
P. Abreu, E. Guerra and Á. Plaza : Proof without words: Limit of a recursive sequence
y = x
y = x/2+2/x
2
2 x3x2
x1
Figure 2. 2 < x0 < +∞
PILAR ABREU, ESTHER GUERRA AND ÁNGEL PLAZA
DEPARTMENT OF MATHEMATICS
UNIVERSITY OF LAS PALMAS DE GRAN CANARIA
EDIFICIO DE INFORMÁTICA Y MATEMÁTICAS
35017–LAS PALMAS DE GRAN CANARIA
SPAIN
E-mail:
aplaza@dmat.ulpgc.es
(Received January, 2005)
x0