The probability of that event is 1/n, which clearly goes to zero...
let Xn , n= 1, 2, . . . . . be a sequence of r.v st
p(Xn = a) = 1 - (1/n), a in R
p(Xn = n^k) = 1/n k>1 , k fixed
show Xn is consitent a consistant estimator for a.
i.e show for all e>0 p(|Xn - a|>= e) tends to 0 as n tends to infinity
thanks for you help