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USAMO
1981
Problem - 3494
If
x
is a positive real number, and
n
is a positive integer, prove that
[
n
x
]
>
[
x
]
1
+
[
2
x
]
2
+
[
3
x
]
3
+
⋯
+
[
n
x
]
n
,
where
[
t
]
denotes the greatest integer less than or equal to
t
. For example,
[
π
]
=
3
and
[
√
2
]
=
1
.
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