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Mar 15, 2020 at 13:28 vote accept Luca
Mar 15, 2020 at 13:05 comment added user6976 No it does not. If you want all $a_n$ to be dfferent in absolute value, add any other series where the sum is 0 and the terms converge to 0 faster than $1/n^4$.
Mar 15, 2020 at 12:53 comment added Luca but doesn't your $a_n$ in fact resemble a bit too closely 0+0+0+0+.... ? thanks anyway, as you made me realize that I shall perhaps better reformulate my question with more constraints on ${a_n}$
Mar 15, 2020 at 12:37 history answered user6976 CC BY-SA 4.0