Take the equation k = (n/2-1)/n, and consider that your k is not fitting into a float (most probably they are using doubles, i.e. the 64-bit floats, but I haven't checked), so k is (apparently) rounded to 0.5. Then, depending on how you transform the equation and the exact step at which you substitute your value for k, you either get -Infinity or -1 (exercise left to the reader, or I guess you could just check the step-by-step solution, but I haven't).
That is how floating point works: you'd rather ideally use arbitrary-precision rationals, otherwise, as mentioned already in the thread, increase the precision of your floating point numbers. But I do not think you can do any of these with Wolfram Alpha.