From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Sat, 1 Mar 1997 19:17:18 -0600 (CST)
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) = 10^5.
sorry. Sum(k=2 ton+1)(1/k) = 10^5.
Since the sum diverges, there is clearly a solution.
Regards,
Jack