Show that if x ∼ geom(p) then p(x = n + k|x > n) = p(x = k), for every n, k ≥ 1. this one of the ways to define the memoryless property of the geometric distribution. it states the following: given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.