Hello everyone im new to this site so hope I am posting in the right place etc. Im struggling with the following question, I just really dont know how to get started, any help would be appreciated!

By considering appropriate series expansions, prove that:

e^{x}* e^{(}^{x^2)/2}* e^{(}^{x^3)/3}* .... = 1 + x + x^{2}+ .... when |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