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# [Vyxal](https://github.com/Vyxal/Vyxal/tree/version-2), 7 bytes 

```
ɾĖ∑?≥)ṅ
```

[Try it Online!](https://vyxal.pythonanywhere.com/?v=2&c=1#WyIiLCIiLCLJvsSW4oiRP+KJpSnhuYUiLCIiLCIzIl0=) Vyxal has arbitrary-precision rationals, so this will never run into precision errors.

```
      ṅ # Find the first integer
-----)  # where
  ∑     # sum of
 Ė      # reciprocals of
ɾ       # range from 1 to n inclusive
    ≥   # is at least
   ?    # the input
```