The negative binomial distribution is unimodal with a mode at the integer part of (k 1)/k. Show that the mode is 0 when

The negative binomial distribution is unimodal with a mode at the integer part of µ(k – 1)/k. Show that the mode is 0 when µ ≤ 1, and that when µ > 1 the mode is still 0 if k < µ/(µ – 1). (This gives greater scope than the Poisson, since its mode equals the integer part of the mean.)