Can somebody help with this question please?
(e^x)(e^x2/2)(e^x^3/3)...=1+x+x^2+... when |x|<1.
Show that the coefficient of x^19 in the power series expansion on the LHS has the form
1/19! + 1/19 + r/s,
where 19 does not divide s.
Deduce that 18!= -1(mod 19).