MathDB
Least alpha for which this sequence is positive

Source: Mediterranean MO 2012 Q1

June 28, 2013
algebra unsolvedalgebra

Problem Statement

For a real number α>0\alpha>0, consider the infinite real sequence defined by x1=1x_1=1 and \alpha x_n = x_1+x_2+\cdots+x_{n+1} \mbox{\qquad for } n\ge1. Determine the smallest α\alpha for which all terms of this sequence are positive reals. (Proposed by Gerhard Woeginger, Austria)
Back to ProblemsView on AoPS