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