# 2015-3 Limit

Let $$\{a_n\}$$ be a sequence of non-negative reals such that $$\lim_{n\to \infty} a_n \sum_{i=1}^n a_i^5=1$$. Prove that $\lim_{n\to \infty} a_n (6n)^{1/6} = 1.$

GD Star Rating