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Problem
Problem
The value of
lim
n
→
∞
n
−
n
2
[
(
n
+
1
)
(
n
+
1
2
)
(
n
+
1
2
2
)
⋯
(
n
+
1
2
n
−
1
)
]
n
\lim_{n \to \infty} n^{-n^2} \left[ (n+1) \left( n + \frac{1}{2} \right) \left( n + \frac{1}{2^2} \right) \cdots \left( n + \frac{1}{2^{n-1}} \right) \right]^n
lim
n
→
∞
n
−
n
2
[
(
n
+
1
)
(
n
+
2
1
)
(
n
+
2
2
1
)
⋯
(
n
+
2
n
−
1
1
)
]
n
is a.
e
e
e
b.
e
2
e^2
e
2
c.
e
3
e^3
e
3
d.
e
4
e^4
e
4
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