MathDB

Problem 4

Part of 2002 VJIMC

Problems(2)

writing numbers around circle, minimal sum

Source: VJIMC 2002 1.4

7/17/2021
The numbers 1,2,…,n1,2,\ldots,n are assigned to the vertices of a regular nn-gon in an arbitrary order. For each edge, compute the product of the two numbers at the endpoints and sum up these products. What is the smallest possible value of this sum?
inequalities
limit integral with natural parameter is invariant

Source: VJIMC 2002 2.4

7/14/2021
Prove that lim⁡n→∞n2(∫011+xnndx−1)=π212.\lim_{n\to\infty}n^2\left(\int^1_0\sqrt[n]{1+x^n}\text dx-1\right)=\frac{\pi^2}{12}.
calculusintegration