Consider fn (2) given in (2.7) of Example 2.5, i.e.

This is a second-order homogeneous difference equation for which a closedform solution can be easily found. Do so, and also check that ∞
i=1
fi = 1 and ∞
i=1 ifi = p−1 + p−2 (use of a symbolic software package is recommended!).
The latter is the expected value, discussed in Chapter 4.

= fnafn-1+qpfn-2. fi=0, f2= p.