Make Egyptian fractions a little more robust.

Add checking for negative arguments, and arguments > 1

Don't know if this is actually needed; it does help avoid endless loops if you give an improper fraction to some of the algorithms.  Feel free to reject.
> Using the divergent sequence is called the Harmonic method there, and changes things greatly (computing 100+1/4 would involve gigantic denominators, just to get up that high).

This could be a problem for practice, but that's all.

> Either we should allow each individual algorithm to handle large inputs in its own way

Can't we just use this "Harmonic method" and switch to the actual algorithm for `0<r<1`?