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Lebl-Basic-Analysis-I
· Problem 2.2.14
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
Suppose
x
1
:
=
c
x_1 := c
x
1
:=
c
and
x
n
+
1
:
=
x
n
2
+
x
n
x_{n+1} := x_n^2 + x_n
x
n
+
1
:=
x
n
2
+
x
n
. Show that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges if and only if
−
1
≤
c
≤
0
-1 \leq c \leq 0
−
1
≤
c
≤
0
, in which case it converges to 0.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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