Consider the sum $S_n = 1 + \frac13 + \frac15 + ... + \frac{1}{2n-1}$. How do we find its sum with accuracy up to $o(1)$?
2026-03-25 04:40:50.1774413650
Find the value of the sum with accuracy up to $o(1)$.
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$$ S_n = H_{2n}-\frac{1}{2}H_n = \log(2n)-\frac{1}{2}\log(n)+\frac{\gamma}{2}+o(1) = \frac{1}{2}\log(n)+\log(2)+\frac{\gamma}{2}+o(1) $$ follows from the well-known asymptotics for harmonic numbers.