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Hi Uri:
I finally looked into your posted solution (of the Leigh's worm problem).
I compared your non-interative expression for the distance covered by
the bug in n steps
x{n} = (n+1)*(sum from k=1 to k=n of (1/k))
with the iterative formula I was able to derive (posted yesterday).
x{n}=[x{n-1}+1]*(1+1/n)
They lead to identical answers. How did you reason to obtain your
formula from the wording of the problem? How did you recognize the
harmonic series (1+1/2+1/3+1/4+ ...+1/n) in it?
Ludwik Kowalski