Can somebody help with this question please?

Prove that

(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).