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Sum of subsequence, over index set of non-zero density, of monotone divergent sum also diver...

Summary. The answer to your question is "No". But it is "Yes" under the additional condition that $\liminf_n n x_n > 0$. All of this follows from work of T. Šalát in the 1960s. You find some details b …
Salvo Tringali's user avatar