(a) Plug s = 0, s = 1, s = 2, and s = 3 into Kramers’ relation (Equation 7.113) to obtain formulas for (r^-1), (r), (r²), and (r³). Note that you could continue indefinitely, to find any positive power.
(b) In the other direction, however, you hit a snag. Put in s = -1, and show that all you get is a relation between (r^-2) and (r^-3).
(c) But if you can get  (r^-2) by some other means, you can apply the Kramers relation to obtain the rest of the negative powers. Use Equation 7.57 (which is derived in Problem 7.42) to determine  (r^-3) , and check your answer against Equation 7.66.

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(7.113) 0=\rs[es-a+r]++- 1+ [+s