Session p. 131

\(ExpectedVisits[ϵ_Real, K_] := \((p\_E = 0.25 + ϵ; 
        p\_W = 0.25 - ϵ; p\_N = \(p\_S = 0.25\); w = \(p\_E\) p\_W; 
        z = \(p\_N\) p\_S; \((a = 1)\) + 
          Sum[\((a *= \(\(2  k \((2  k - 1)\)\)\/k\^2\) z)\) \((\((b = 1)\) + 
                  Sum[b *= \(\((\(k - j + 1\)\/j)\)\^2\) w\/z, {j, 1, 
                      k}])\), {k, 1, 
              K - 1}])\); \({K == #, \(ϵ\_*\) == \((ϵ /. FindRoot[ExpectedVisits[ϵ, #] == 2, {ϵ, 0.06, 
                      0.07}, WorkingPrecision -> MachinePrecision, 
                    PrecisionGoal -> 12\ ])\)} &\) /@ {125, 250, 500, 
          1000} // TableForm\)