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Brazil Undergrad MO
2005 Brazil Undergrad MO
4
Convergence - beautifull
Convergence - beautifull
Source: Obm - 2005
October 23, 2005
logarithms
limit
ratio
real analysis
real analysis unsolved
Problem Statement
Let
a
n
+
1
=
a
n
+
1
a
n
2005
a_{n+1} = a_n + \frac{1}{{a_n}^{2005}}
a
n
+
1
=
a
n
+
a
n
2005
1
and
a
1
=
1
a_1=1
a
1
=
1
. Show that
∑
n
=
1
∞
1
n
a
n
\sum^{\infty}_{n=1}{\frac{1}{n a_n}}
∑
n
=
1
∞
n
a
n
1
converge.
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