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National and Regional Contests
Moldova Contests
Moldova National Olympiad
2007 Moldova National Olympiad
11.2
Find Limit
Find Limit
Source: Moldova National MO, XI Class, 2007
March 3, 2007
limit
logarithms
calculus
calculus computations
Problem Statement
Define
a
n
a_{n}
a
n
as satisfying:
(
1
+
1
n
)
n
+
a
n
=
e
\left(1+\frac{1}{n}\right)^{n+a_{n}}=e
(
1
+
n
1
)
n
+
a
n
=
e
. Find
lim
n
→
∞
a
n
\lim_{n\rightarrow\infty}a_{n}
lim
n
→
∞
a
n
.
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