find the variance

Question

I am trying to find the E[N] when p_{n} = p_{n-1}{a +( b/n)) for n =3,4,… in terms of a and b.  I tried to multiply both sides by n and sum over the space starting at n = 3 to get the expectation of N.  But p_{n} is defined on n = 0,1,2,…  Not sure where to start my indices in my sums to get the expectation.  I also need to find the variance as well.

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