In a game the bank will pay nothing with probability 0.8 = f(0), and will pay $n with p.m.f. (probability mass function) f(n) = af(n-1)/n for n=1,2,3... (infinity)

1- find the constant a.

2- Find the probability, that the bank pays $1.

3- Find the probability the bank pays $1 or more.

4- Find the probability the expected payment of the bank.

5- Find the variance of the bank.

6- If it costs a quarter to play, should you play?

I'm so lost and not sure what kind of infinite sum this is. Any help will be greatly appreciated!!!