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2010 VTRMC
Problem 6
limit of sequence
limit of sequence
Source: VTRMC 2010 P6
May 17, 2021
Sequences
limit
real analysis
Problem Statement
Define a sequence by
a
1
=
1
,
a
2
=
1
2
a_1=1,a_2=\frac12
a
1
=
1
,
a
2
=
2
1
, and
a
n
+
2
=
a
n
+
1
−
a
n
a
n
+
1
2
a_{n+2}=a_{n+1}-\frac{a_na_{n+1}}2
a
n
+
2
=
a
n
+
1
−
2
a
n
a
n
+
1
for
n
n
n
a positive integer. Find
lim
n
→
∞
n
a
n
\lim_{n\to\infty}na_n
lim
n
→
∞
n
a
n
.
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