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Mathematics
Problem
Evaluate the limit
lim
n
→
∞
[
1
n
∑
i
=
1
n
i
n
+
1
n
∑
i
=
n
+
1
2
n
3
]
.
\lim_{n\to\infty}\left[\,\frac{1}{n}\sum_{i=1}^{n}\frac{i}{n}+\frac{1}{n}\sum_{i=n+1}^{2n}3\,\right].
n
→
∞
lim
[
n
1
i
=
1
∑
n
n
i
+
n
1
i
=
n
+
1
∑
2
n
3
]
.
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