>>70
f(x) = Σ_{k=0 to ∞} (x^k) = 1/(1-x)

(d/dx) f(x) = Σ k (x^(k-1)) = 1/(1-x)^2
Σ k ((1/3)^(k-1)) = 1/(1-(1/3))^2 = 9/4
Σ k ((1/3)^k) = 1/(1-(1/3))^2 = 3/4

E[pk] = (2/3) Σ k (1/3)^k = 1/2