證明：設(shè){an}為等差數(shù)列an=a+(n-1)d
則{1/an}為1/a,1/(a+d),1/(a+2d),……,1/(a+nd),……
當(dāng)d=0時(shí){1/an}為常數(shù)列{1/a}顯然發(fā)散
當(dāng)d≠0時(shí),設(shè)bn={1/(nd)}
因?yàn)閘im(1/an)/bn=limnd/(a+(n-1)d)=1,而級(jí)數(shù){1/nd}=1/d{1/n}發(fā)散
根據(jù)比較審斂法{1/an}發(fā)散
證畢!