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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
134
Today's calculation of Integral 134
Today's calculation of Integral 134
Source: Chiba University entrance exam 1968
August 10, 2006
calculus
integration
limit
logarithms
calculus computations
Problem Statement
For positive integers
n
,
n,
n
,
let
A
n
=
1
n
{
(
n
+
1
)
+
(
n
+
2
)
+
⋯
+
(
n
+
n
)
}
,
B
n
=
{
(
n
+
1
)
(
n
+
2
)
⋯
(
n
+
n
)
}
1
n
.
A_{n}=\frac{1}{n}\{(n+1)+(n+2)+\cdots+(n+n)\},\ B_{n}=\{(n+1)(n+2)\cdots (n+n)\}^{\frac{1}{n}}.
A
n
=
n
1
{(
n
+
1
)
+
(
n
+
2
)
+
⋯
+
(
n
+
n
)}
,
B
n
=
{(
n
+
1
)
(
n
+
2
)
⋯
(
n
+
n
)
}
n
1
.
Find
lim
n
→
∞
A
n
B
n
.
\lim_{n\to\infty}\frac{A_{n}}{B_{n}}.
lim
n
→
∞
B
n
A
n
.
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