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Putnam
2006 Putnam
B6
Putnam 2006 B6
Putnam 2006 B6
Source:
December 4, 2006
Putnam
limit
factorial
Harvard
college
inequalities
integration
Problem Statement
Let
k
k
k
be an integer greater than
1.
1.
1.
Suppose
a
0
>
0
a_{0}>0
a
0
>
0
and define
a
n
+
1
=
a
n
+
1
a
n
k
a_{n+1}=a_{n}+\frac1{\sqrt[k]{a_{n}}}
a
n
+
1
=
a
n
+
k
a
n
1
for
n
≥
0.
n\ge 0.
n
≥
0.
Evaluate
lim
n
→
∞
a
n
k
+
1
n
k
.
\lim_{n\to\infty}\frac{a_{n}^{k+1}}{n^{k}}.
n
→
∞
lim
n
k
a
n
k
+
1
.
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