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Laurențiu Panaitopol, Tulcea
2010 Laurențiu Panaitopol, Tulcea
1
Limit of stacked cubic roots
Limit of stacked cubic roots
Source:
October 28, 2019
Sequences
limits
real analysis
Weierstrass
Nested Radicals
Problem Statement
Show that if
(
s
n
)
n
≥
0
\left( s_n \right)_{n\ge 0}
(
s
n
)
n
≥
0
is a sequence that tends to
6
,
6,
6
,
then, the sequence
(
s
n
+
s
n
−
1
+
s
n
−
2
+
⋯
+
s
0
3
3
3
3
3
)
n
≥
0
\left( \sqrt[3]{s_n+\sqrt[3]{s_{n-1}+\sqrt[3]{s_{n-2}+\sqrt[3]{\cdots +\sqrt[3]{s_0}}}}} \right)_{n\ge 0}
3
s
n
+
3
s
n
−
1
+
3
s
n
−
2
+
3
⋯
+
3
s
0
n
≥
0
tends to
2.
2.
2.
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