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Problem
Problem
If
[
x
]
[x]
[
x
]
denotes the integral part of
x
x
x
for real
x
x
x
, then find the value of
[
1
4
]
+
[
1
4
+
1
200
]
+
[
1
4
+
2
200
]
+
[
1
4
+
3
200
]
+
⋯
+
[
1
4
+
199
200
]
.
\left[ \frac{1}{4} \right] + \left[ \frac{1}{4} + \frac{1}{200} \right] + \left[ \frac{1}{4} + \frac{2}{200} \right] + \left[ \frac{1}{4} + \frac{3}{200} \right] + \dots + \left[ \frac{1}{4} + \frac{199}{200} \right].
[
4
1
]
+
[
4
1
+
200
1
]
+
[
4
1
+
200
2
]
+
[
4
1
+
200
3
]
+
⋯
+
[
4
1
+
200
199
]
.
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