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Lebl-Basic-Analysis-I
· Problem 2.2.4
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
Suppose
x
1
:
=
1
2
x_1 := \frac{1}{2}
x
1
:=
2
1
and
x
n
+
1
:
=
x
n
2
x_{n+1} := x_n^2
x
n
+
1
:=
x
n
2
. Show that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges and find
lim
n
→
∞
x
n
\lim_{n\to\infty} x_n
lim
n
→
∞
x
n
. Hint: You cannot divide by zero!
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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