{"schema":"vela.problem-packet.v0.1","problem":314,"statement":"Let $n\\geq 1$ and let $m$ be minimal such that $\\sum_{n\\leq k\\leq m}\\frac{1}{k}\\geq 1$. We define\\[\\epsilon(n) = \\sum_{n\\leq k\\leq m}\\frac{1}{k}-1.\\]How small can $\\epsilon(n)$ be? Is it true that\\[\\liminf n^2\\epsilon(n)=0?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}