New posts in nonlinear-dynamics

2D bifurcation problem

dynamical-systems self-learning nonlinear-analysis nonlinear-dynamics bifurcation

Given $(a_n)$ such that $a_1 \in (0,1)$ and $a_{n+1}=a_n+(\frac{a_n}{n})^2$. Prove that $(a_n)$ has a finite limit. [duplicate]

real-analysis sequences-and-series convergence-divergence recurrence-relations nonlinear-dynamics