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However, I have no idea where to begin
2026-05-05 18:39:14.1778006354
trying to prove or disprove $C$ for the sequence: $\forall c \in N : S_n = n^2 - n$
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The point here is that the choice of $m$ comes at the very end. We can always choose $m=\frac {k^{165}+165} {S_k}$ so that the inequality holds. [ We can take $i=1$]. Hence $C$ is true.