Let Z₁, Z2,... be a sequence of random variables, and suppose that for n = 2, 3,..., the distribution of Zn is as follows: P(Zn = 1/n) = 1-1/n², P(Zn = n) = 1/n².

(a) Does there exist a constant c to which the sequence converges in probability?
(b) Does there exist a constant c to which the sequence converges in quadratic mean?