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Results tagged with divergent-series
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user 475875
6
votes
Accepted
Series convergence if $\sum a_n^2 < \infty$
I think the answer is no.
By functional analysis, we know that it suffices to show the existence of a sequence $a_n$ such that $\lVert a \rVert_2 = 1$ and
$$\sum_{n = 1}^{\infty} \left(\sum_{j = 1}^\i …
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