The right hand side is a geometric series that sums to 1/(1- x).

The exponetials on the left can be combined to give and you should recogize that exponent as the Taylor's series for ln(x) about x= 1.

By expanding each individual exponential term on the left-hand side and multiplying out, show that the coeﬃcient of x^{19}has the form:

1/19! + 1/19 + r/s, where 19 does not divide s.

Thanks

LexiBelle