Consider the function defined as follows 1 1(k) = for k1. k(k+1) a) Determine the partial sum Un = k=1(k). b) Calculate limn Un c) Verify that is a probability mass function. Let X be a random variable with probability mass function y. P(X = k) = (k), with k1 Determine a) the probability that the event {X = 2} occurs. c) the probability of the event (X 2}.