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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 53
Find the limit of this summation
Find the limit of this summation
Source: 2019 Jozsef Wildt International Math Competition
May 20, 2020
limit
Summation
calculus
Problem Statement
Compute
lim
n
→
∞
1
n
∑
k
=
1
n
n
+
1
n
+
k
+
1
−
n
n
+
k
n
+
1
n
+
k
−
n
n
+
k
\lim \limits_{n \to \infty}\frac{1}{n}\sum \limits_{k=1}^n\frac{\sqrt[n+k+1]{n+1}-\sqrt[n+k]{n}}{\sqrt[n+k]{n+1}-\sqrt[n+k]{n}}
n
→
∞
lim
n
1
k
=
1
∑
n
n
+
k
n
+
1
−
n
+
k
n
n
+
k
+
1
n
+
1
−
n
+
k
n
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