Let r(k) = [k + 1/2] = k rounded to the nearest integer. For integer n >= 0, define the sequence S(k) = { r(k/2^n) : n >= 1 } So, for example, we have f(11) = (r(11/2), r(11/4), r(11/8), ...) = (6, 3, 1, 1, 0, 0, 0, ...) What are SUM(k = 1..inf, f(k)) SUM(k = 1..inf, 2^k f(k)^2)