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VTRMC
2013 VTRMC
Problem 3
convergence of sequence
convergence of sequence
Source: VTRMC 2013 P3
May 12, 2021
Sequences
real analysis
Problem Statement
Define a sequence
(
a
n
)
(a_n)
(
a
n
)
for
n
≥
1
n\ge1
n
≥
1
by
a
1
=
2
a_1=2
a
1
=
2
and
a
n
+
1
=
a
n
1
+
n
−
3
/
2
a_{n+1}=a_n^{1+n^{-3/2}}
a
n
+
1
=
a
n
1
+
n
−
3/2
. Is
(
a
n
)
(a_n)
(
a
n
)
convergent (i.e.
lim
n
→
∞
a
n
<
∞
\lim_{n\to\infty}a_n<\infty
lim
n
→
∞
a
n
<
∞
)?
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