taylor series, bfloat, zerop enhancements, something to think about, vs. Macsyma

taylor(((n - 1/2)*(%e^(1/n) - 1))^n, n, inf, 3);

says "an error ..."

though in Macsyma, the answer comes out as
1 - (1/(12 * n)) - (11/(288 * n^2)) - (653/(51840 * n^3)) + . . .

also, bfloat(1/3,100)  gives 100 digits of 1/3.  Maxima's bfloat
ignores 2nd. argument.

Maxima has no zerop() function.  I think it could be defined as..

   zerop(x):=if bfloatp(x) then ?zerop(?cadr (x))
             else if ?numberp(x) then ?zerop(x)
             else if ratp(x) then ?equal(0, ?cadr (x))
             else false

RJF