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,
loading...
KAIST Math Problem of the Week
Weekly Math Challenges in KAIST
The statement is false without extra conditions on the sequence, since if $latex \{a_n\}$ satisfies the problem, then $latex \{-a_n\}$ does, too.
Thanks for pointing it out. Please assume that a_n is nonnegative.