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Unirea
2005 Unirea
3
math contest 3
math contest 3
Source: Unirea 2005
February 8, 2005
real analysis
real analysis unsolved
Problem Statement
a
1
=
b
1
=
1
a_1=b_1=1
a
1
=
b
1
=
1
a
n
+
1
=
b
n
+
1
n
a_{n+1}=b_n+\frac{1}{n}
a
n
+
1
=
b
n
+
n
1
b
n
+
1
=
a
n
−
1
n
b_{n+1}=a_n-\frac{1}{n}
b
n
+
1
=
a
n
−
n
1
Prove that
a
n
a_n
a
n
,
b
n
b_n
b
n
is not convergent, but
a
n
b
n
a_nb_n
a
n
b
n
is convergent Laurentin Panaitopol
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