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Mathematics
Mathematics
Problem
Rewrite the limit
lim
n
→
∞
∑
k
=
1
n
ln
(
1
+
2
k
n
)
2
n
\lim_{n\to\infty}\sum_{k=1}^{n}\ln\!\left(1+\frac{2k}{n}\right)\frac{2}{n}
n
→
∞
lim
k
=
1
∑
n
ln
(
1
+
n
2
k
)
n
2
as a single definite integral in
x
x
x
. Do not evaluate the integral.
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