Let $(a_n)$ and $(b_n)$ be sequences of positive real numbers. Denote by $o$ the "little-oh" Landau symbol. Is it possible, in general, to find a third sequence $(c_n)$ such that $\sum_{k=0}^n a_k = o(b_n)$ if and only if $a_n = o(c_n)$? Is there a formula for such a $(c_n)$ in terms of $(a_n)$ and $(b_n)$?
2026-04-09 15:18:33.1775747913
Asymptotic growth bound on a sequence equivalent to an asymptotic growth bound on its sum.
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