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If
U
n
=
(
1
+
1
n
2
)
(
1
+
2
2
n
2
)
2
⋯
(
1
+
n
2
n
2
)
n
U_n = \left(1 + \frac{1}{n^2}\right) \left(1 + \frac{2^2}{n^2}\right)^2 \cdots \left(1 + \frac{n^2}{n^2}\right)^n
U
n
=
(
1
+
n
2
1
)
(
1
+
n
2
2
2
)
2
⋯
(
1
+
n
2
n
2
)
n
…
Mathematics
Problem
If
U
n
=
(
1
+
1
n
2
)
(
1
+
2
2
n
2
)
2
⋯
(
1
+
n
2
n
2
)
n
U_n = \left(1 + \frac{1}{n^2}\right) \left(1 + \frac{2^2}{n^2}\right)^2 \cdots \left(1 + \frac{n^2}{n^2}\right)^n
U
n
=
(
1
+
n
2
1
)
(
1
+
n
2
2
2
)
2
⋯
(
1
+
n
2
n
2
)
n
, then
lim
n
→
∞
(
U
n
)
−
4
n
2
\lim_{n \to \infty} (U_n)^{\frac{-4}{n^2}}
lim
n
→
∞
(
U
n
)
n
2
−
4
is equal to a.
e
2
/
16
e^2/16
e
2
/16
b.
4
/
e
4/e
4/
e
c.
16
/
e
2
16/e^2
16/
e
2
d.
4
/
e
2
4/e^2
4/
e
2
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