证明:当n=2时,左边=1-1/2=1/2,右边=2(1/(2+2))=1/2,左边=右边,成立 假设当n=2k时,成立,即1-1/2+1/3.+1/(2k-1)-1/2k=2[1/(2k+2)+(1/2k+4)+.+1/(4k)] 则当n=2k+2时,左边=1-1/2+1/3.+1/(2k-1)-1/2k+1/(2k+1)-1/(2k+2) ...