>>838
S = Σ_{k=1 to ∞} (1/2^k) (k+1)
(1/2)S = Σ_{k=1 to ∞} (1/2^(k+1)) (k+1)
= Σ_{k=2 to ∞} (1/2^k) k

S - (1/2)S = 1 + Σ_{k=2 to ∞} (1/2^k) = 1 + (1/2) = 3/2
(1/2) S = 3/2
S = 3