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Mathematics
Mathematics
Problem
Compute
lim
n
→
∞
n
(
n
+
1
−
n
)
\displaystyle\lim_{n\to\infty} \sqrt{n}\bigl(\sqrt{n+1}-\sqrt{n}\bigr)
n
→
∞
lim
n
(
n
+
1
−
n
)
and determine the implication for convergence or divergence of the series
∑
n
=
1
∞
n
(
n
+
1
−
n
)
\displaystyle\sum_{n=1}^{\infty} \sqrt{n}\bigl(\sqrt{n+1}-\sqrt{n}\bigr)
n
=
1
∑
∞
n
(
n
+
1
−
n
)
.
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