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+1依然成立
所以对一切n属于N+都成立 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+1依然成立
所以对一切n属于N+都成立