IMO Shortlist 1995 problem S4


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 7,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Suppose that x_1, x_2, x_3, \ldots are positive real numbers for which x^n_n = \sum^{n-1}_{j=0} x^j_n for n = 1, 2, 3, \ldots Prove that \forall n, 2 - \frac{1}{2^{n-1}} \leq x_n < 2 - \frac{1}{2^n}.
Izvor: Međunarodna matematička olimpijada, shortlist 1995