Problem #PRU-61306

Problems Algebra Sequences Recurrent relations Number sequences Boundedness, monotonicity Recurrent relations (other) Calculus

Problem

The sequence of numbers \(a_n\) is given by the conditions \(a_1 = 1\), \(a_{n + 1} = a_n + 1/a^2_n\) (\(n \geq 1\)).

Is it true that this sequence is limited?