I know that $$\sum_{n\leq x}\log(n)=x\log(x)-x+O(\log(x))$$ but I read (in a proof of a theorem ) the following formula $$\sum_{n\leq x}\log(n)=x\log(x)+O(x)$$ Why are the two forms equal?
2026-05-04 10:01:04.1777888864
The partial sums of $\log n$
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