当n=1时,左边=1^2/(1*3)=1/3,右边=1*2/(2*3)=1/3成立假设当n=K时1^2/(1*3)+2^2/(3*5)+...+k^2/(2k-1)(k+1)=k(k+1)/[2(2k+1)] 成立当n=k+1时左边=k(k+1)/[2(2k+1)] +(k+1)^2/(2k+1)(k+2)=(k+1)(k+2)/[2(2k+3)]=(k+1)[...左边=k(k+1)/[2(2k+1)] +(k+1)^2/(2k+1)(k+2) 怎么得出的？k(k+1)/[2(2k+1)] 是n=k时的值,后面的是n=k+1时,比n=k时多的项