因为1/3+1/4>2*(1/4)=1/21/5+1/6+..+1/8>4*1/8=1/21/9+1/10+..+1/16>8*1/16=1/2...1/[2^(n-1)+1]+1/[2^(n-1)+2]+..+1/(2^n)>1/2...而1/(4^1000)=1/(2^2000)所以1+1/2+1/3+1/4+..+1/(2^2000)>1+2000*(1/2)=1001>1000...