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
loading...
2015-3 Limit, 3.5 out of 5 based on 12 ratings

2 thoughts on “2015-3 Limit

  1. LJW

    The statement is false without extra conditions on the sequence, since if $latex \{a_n\}$ satisfies the problem, then $latex \{-a_n\}$ does, too.

Comments are closed.