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Nicolae Coculescu
2004 Nicolae Coculescu
2
Sequence defined with powers of the order $ 1/n $
Sequence defined with powers of the order $ 1/n $
Source:
December 14, 2019
real analysis
Sequences
limits
Problem Statement
Let bet a sequence
(
a
n
)
n
≥
1
\left( a_n \right)_{n\ge 1}
(
a
n
)
n
≥
1
with
a
1
=
1
a_1=1
a
1
=
1
and defined as
a
n
=
1
+
n
a
n
−
1
n
.
a_n=\sqrt[n]{1+na_{n-1}} .
a
n
=
n
1
+
n
a
n
−
1
.
Show that
(
a
n
)
n
≥
1
\left( a_n \right)_{n\ge 1}
(
a
n
)
n
≥
1
is convergent and determine its limit. Florian Dumitrel
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