(1) Prove that the sequence {} 4n2-2n100 converges to 4/3. arctan(n)}=1 does not converge. (2) Prove that the sequence {; (-1)" (3) Suppose that {s} is a sequence of real numbers such that (a) for every N = N there exists n₁, n₂ > N such that S <0 and 8n2 > 0, and (b) {8} is convergent. Prove that lim 8,, = 0. (4) Let t₁ =1, and t+1 = Sn tn for n ≥ 1, where {s} is a positive strictly mo increasing sequence with lim s₁ = 1. (a) Show that limt, exists.