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Mathematics
Mathematics
Problem
For each positive integer
n
n
n
, let
y
n
=
1
n
(
(
n
+
1
)
(
n
+
2
)
…
(
n
+
n
)
)
1
n
y_n = \frac{1}{n} \left( (n+1)(n+2)\dots(n+n) \right)^{\frac{1}{n}}
y
n
=
n
1
(
(
n
+
1
)
(
n
+
2
)
…
(
n
+
n
)
)
n
1
. For
x
∈
R
x \in \mathbb{R}
x
∈
R
, let
[
x
]
[x]
[
x
]
be the greatest integer less than or equal to
x
x
x
. If
lim
n
→
∞
y
n
=
L
\lim_{n \to \infty} y_n = L
lim
n
→
∞
y
n
=
L
, then the value of
[
L
]
[L]
[
L
]
is _____.
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