MathDB

2020 BMT Team 24

Source:

January 9, 2022

algebracombinatorics

Problem Statement

For positive integers

N

and

m

, where

m \le N

, define

a_{m,N} =\frac{1}{{N+1 \choose m}} \sum_{i=m-1}^{N-1} \frac{ {i \choose m-1}}{N - i}

Compute the smallest positive integer

N

such that

\sum^N_{m=1}a_{m,N} >\frac{2020N}{N +1}