令a(n)=1+1/2+1/3+.+1/2^n则a(n+1)=1+1/2+1/3+.+1/2^n+1/(2^n+1)+1/(2^n+2)+...+1/2^(n+1)先证明左边：当n=1时,a(n)=1+1/2=3/2;显然a(1)>=1+1/2设当n=k(k>1,k属于正整数）时,a(k)>=1+k/2则当n=k+1时,a(k+1)=1+1/2+1/...