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Nexus[Free-DC]
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This thing has me tearing my hair out:
Let {a0, a1,...} 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?
Let {a0, a1,...} 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?