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Problem
Problem
Evaluate
lim
n
→
∞
[
x
]
+
[
2
x
]
+
[
3
x
]
+
⋯
+
[
n
x
]
n
2
\lim_{n \to \infty} \frac{[x] + [2x] + [3x] + \dots + [nx]}{n^2}
lim
n
→
∞
n
2
[
x
]
+
[
2
x
]
+
[
3
x
]
+
⋯
+
[
n
x
]
where
[
⋅
]
[\cdot]
[
⋅
]
denotes the greatest integer function.
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