Given p ∈ ℝ⁺, call a real sequence [tex]\rm \{a_n \}^{ \infty }_{n = 1}[/tex] p-rapid if, for any є > 0, there exists N ∈ ℤ⁺ such that
[tex] \rm | a_{n + 1} - a_{n} | < \frac{ \epsilon}{ {n}^{p} } [/tex] for any positive integer n≥N.
For what values of p > 0, if any, does a real sequence being p-rapid imply its convergence?​