MathDB
Problems
Contests
Undergraduate contests
IMC
2020 IMC
8
IMC 2020 Problem 8
IMC 2020 Problem 8
Source: IMC 2020
July 28, 2020
IMC
real analysis
binomial coefficients
logarithms
IMC 2020
Problem Statement
Compute
lim
n
→
∞
1
log
log
n
∑
k
=
1
n
(
−
1
)
k
(
n
k
)
log
k
.
\lim\limits_{n \to \infty} \frac{1}{\log \log n} \sum\limits_{k=1}^n (-1)^k \binom{n}{k} \log k.
n
→
∞
lim
l
o
g
l
o
g
n
1
k
=
1
∑
n
(
−
1
)
k
(
k
n
)
lo
g
k
.
Back to Problems
View on AoPS