Problems

In Problems 1-8, find the nth term of the sequence.

Determine whether the following sequences converge, and find the limits when they exist.

30            Formulate an ε, δ condition for lim_n→∞ a_n = -∞.

31             Show that if lim_n→∞ a_n = L and lim_n→∞ b_n = M then lim_n→∞ (a_n + b_n) = L + M.

32            Show that if lim_n→∞ a_n = L then lim_n→∞ ca_n = cL.