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Today's Calculation Of Integral
2011 Today's Calculation Of Integral
724
Today's calculation of Integral 724
Today's calculation of Integral 724
Source: 2007 Kochi University entrance exam
June 27, 2011
calculus
integration
limit
logarithms
calculus computations
Problem Statement
Find
lim
n
→
∞
{
(
1
+
n
)
1
n
(
1
+
n
2
)
2
n
(
1
+
n
3
)
3
n
⋯
⋯
2
}
1
n
\lim_{n\to\infty}\left\{\left(1+n\right)^{\frac{1}{n}}\left(1+\frac{n}{2}\right)^{\frac{2}{n}}\left(1+\frac{n}{3}\right)^{\frac{3}{n}}\cdots\cdots 2\right\}^{\frac{1}{n}}
lim
n
→
∞
{
(
1
+
n
)
n
1
(
1
+
2
n
)
n
2
(
1
+
3
n
)
n
3
⋯⋯
2
}
n
1
.
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