Ivan Shishkin, Rye (1878)

Problems/Linear algebraUnreviewed

Problème 4 des IMO 1988

by Uettechat·
60
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Montrer que l’ensemble {x∈R,∑k=170kx−k≥5/4}\displaystyle \left\{ x \in \mathbb{R} , \sum_{k=1}^{70} \frac{k}{x-k} \geq 5/4 \right\} est réunion d’ensemble disjoints dont la somme des longueurs vaut 1988.

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