证明Sn=1+1/2+1/3+………+1/n是发散的?

Question

证明Sn=1+1/2+1/3+………+1/n是发散的?

Answer 1

Sn=1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+……
>1+1/2+(1/4+1/4)+(1/8+1/8+1/8+1/8)+……
＝1+1/2+1/2+1/2+……
当然是发散级数.