MathDB

A3

Part of 2020 Simon Marais Mathematics Competition

Problems(1)

number that can be written as a certain series

Source: 2020 Simon Marais Mathematics Competition A3

11/17/2020
Determine the set of real numbers α\alpha that can be expressed in the form α=∑n=0∞xn+1xn3\alpha=\sum_{n=0}^{\infty}\frac{x_{n+1}}{x_n^3} where x0,x1,x2,…x_0,x_1,x_2,\dots is an increasing sequence of real numbers with x0=1x_0=1.
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