lim(n→∞) n[e^(a/n)-e^(b/n)]
= lim(n→∞)[e^(a/n)-e^(b/n)] / (1/n) Heine定理, x = 1/n -> 0
= lim(x→0)[e^(a x)-e^(b x)] / x 洛必达法则
= lim(x->0) [a * e^(a x) -b * e^(b x)]
= a - b