数学的增1法
n=1.2=2.成立.设n=k时成立:(k+1)(k+2).(k+k)=1*3*...*(2k-1)*2^k.看n=k+1:左边=[(k+1)+1][(k+1)+2]……[(k+1)+(k+1)]=[(k+1)(k+2)……(k+k)](k+1+k)(k+1+k+1)/(k+1)=[1*3*...*(2k-1)*2^k](2k+1)[2(k+1)]/(k+1)=1*2*3*……(2k-1)(2k+1)*2^(k+1)=1*2*3*……([2(k+1)-1]*2^(k+1).从数学归纳法,命题对一切自然数n都成立.“从k到k+1”左边需要增乘的代数式是:(k+1)(k+1+k)(k+1+k+1)/(k+1)