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Let $\sum a_{n}$ be an absolutely convergent series such that $$\sum a_{kn}=0$$ for all $k\geq 1$. Help me prove that $a_{n}=0$ for all $n$.

Thank you!

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    What's $a_{kn}$?2011-04-04
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    Please don't post in the imperative; if you are having trouble, the best course of action is to say why or where you are having trouble, and what you have tried or succeeded in doing.2011-04-04
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    If $a_{kn}$ is the subsequence of terms with index multiple of $k$, what happens if you take $k=1$?2011-04-04
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    @Arturo: I edited the question to make it more polite. But this goes right back to the meta thread about editing... Was this change ok or too much?2011-04-04
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    By the way, this is a nice problem.2011-04-04

4 Answers 4