MathDB

1

Part of 2005 Kurschak Competition

Problems(1)

Choice of indexes in a sequence

Source: Kürschák 2005, problem 1

7/13/2014
Let N>1N>1 and let a1,a2,…,aNa_1,a_2,\dots,a_N be nonnegative reals with sum at most 500500. Prove that there exist integers k≥1k\ge 1 and 1=n0<n1<⋯<nk=N1=n_0<n_1<\dots<n_k=N such that ∑i=1kniani−1<2005.\sum_{i=1}^k n_ia_{n_{i-1}}<2005.
probabilityalgebra unsolvedalgebra