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Mathematics
Mathematics
Problem
Evaluate
lim
n
→
∞
(
n
n
+
1
)
n
\displaystyle\lim_{n\to\infty}\left(\dfrac{n}{n+1}\right)^{\!n}
n
→
∞
lim
(
n
+
1
n
)
n
and decide, using that limit, whether the series
∑
n
=
1
∞
(
n
n
+
1
)
n
\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{n}{n+1}\right)^{\!n}
n
=
1
∑
∞
(
n
+
1
n
)
n
converges or diverges.
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