Example 1 (Continued)

lim_n→∞ 1 = 1, converges, because a_H = 1 for all H.

lim_n→∞ n - 2 = ∞, diverges, because H - 2 is positive infinite for all H.

lim_n→∞( - 2n) = - ∞, diverges, because -2H is negative infinite for all H.

lim_n→∞ (-1)ⁿ is undefined, diverges, because(-1)^2H = 1 but(- 1)^2H+1 = - 1.

lim_n→∞ 1/n = 0, converges, because 1/H has standard part zero.