Hi can anybody help?

I am revising generating functions and came across the question.

A player can score 0,1 or 2 points in a game with respective probabilities 1/10,3/5 and 3/10. A sequence of n independent games is played, where n is the value obtained by throwing a fair die. Find the PGF of the total sun of scores obtained by the player and the expectation of the total sum.

In the example they start off by working out GN(s) as equal to

s(1-s^6)/6(1-s). I do not understand how they have got to this. Can anybody help? I am also stuggling with working out the expectation.

Thanks