1-2/3=?
问题描述：
1-2/3=?
(-2/3)*(1-2/4)=?
(-2/3)*(1-2/4)*(1-2/5)=?
猜想:(1-2/3)*(1-2/4)*(1-2/5)...*(1-2/(2+n))
用数学归纳发证明猜想!
答
猜想为2/(n+1)(n+2)当n=1时成立假设对n=k时成立,当 n=k+1时,(1-2/3)*(1-2/4)*(1-2/5)...*(1-2/(3+k))= [(1-2/3)*(1-2/4)*(1-2/5)...*(1-2/(2+k)) ](1-2/(3+k))=2/(k+1)(k+2)*(1-2/(3+k))=2/(k+2)(k+3)所以猜想对n=k+...