For any positive integer $n$ show the inequality holds : $$\left|\sum_{i=1}^{n}\frac{\mu(i)}{i}\right|\le 1$$ I tried induction. when $\mu(n+1)=0$ it is trivial. But what if $\mu(n+1)\ne 0$? I am stuck there. Can someone help me? Thanks.
2026-03-25 09:32:39.1774431159
An inequality involving Möbius function
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