- #1

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Let {a

_{0}, a

_{1},...} be a sequence such that

[tex]\sum_{n=0}^{\infty}{\frac{1}{a_{n}}}[/tex] diverges.

Does [tex]\sum_{n=0}^{\infty}{\frac{1}{a_{a_{n}}}}[/tex] diverge?

My first instinct was to say no, but then I couldn't find any counterexamples. Now I am thinking it might actually be true but it has defied all the tests I've tried. Any ideas?