combinatorial sum
Source: IMO ShortList 1991, Problem 11 (AUS 4)
April 26, 2005
combinatoricsseries summationbinomial coefficientsSummationCombinatorial IdentityIMO Shortlist
Problem Statement
Prove that \sum_{k \equal{} 0}^{995} \frac {( \minus{} 1)^k}{1991 \minus{} k} {1991 \minus{} k \choose k} \equal{} \frac {1}{1991}