f(n)=1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+...
g(n)=1/2+1/2+(1/4+1/4)+(1/8+1/8+1/8+1/8)+...=k/2
f(n)>g(n)
lim(n→∞)g(n)=lim(k→∞)k/2=∞
所以
lim(n→∞)f(n)=∞
f(n)=1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+...
g(n)=1/2+1/2+(1/4+1/4)+(1/8+1/8+1/8+1/8)+...=k/2
f(n)>g(n)
lim(n→∞)g(n)=lim(k→∞)k/2=∞
所以
lim(n→∞)f(n)=∞