1 n=2满足2设n=k-1满足,证n=k满足即可(相减小于一,有2^(k-1)项)
(1)当n=2时 1+1/2+1/3=1+5/6<2 成立(2)设当n=k时 1+1/2+1/3+…+1/(2^k-1) 当n=k+1时 1+1/2+1/3+…+1/[2^(k+1)-1]<k+1/2^k+1/(2^k+1)+...+1/[2^(k+1)-1]<k+ 2^k*(1/2^k)<k+1 成立综合(1)(2)得1+1/2+1/3+…+1/(2^n-1)