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Hi all-
I've barely been following the worm problem, but it doesn't look
ill-formed to me.
The length after n steps is L_n=L_0 + n (in km). with L_0=1.........................................................................
The worm position after n+1 steps is x_(n+1) = x_n + 1 +x_n(1km/L_n).
But L_n = (n+1)km
so x_(n+1) = x_n + 1 + x_n(1/(n+1))
or x_(n+1) - x_n((n+2)/(n+1)) =1
the solution, satisfying the initial conditions is
x_n = (n+1)Sum(k=2 to n+1)(1/k) and
x_n = L_n when Sum(k=2 to n+1)(1/k) = 10^5.
Since the sum diverges, there is clearly a solution.