Question

一道化简题 要详细过程 谢谢

Answer 1

从最后项着手
（n+2)/(n!+(n+1)!+(n+2)!)分子不变，动分母n!+（n+1）！+（n+2）！=n!+n!(n+1)+n!(n+1)(n+2)=n!(1+n+1+(n+1)(n+2))=n!(n2+4n+4)=n!(n+2)2
所以，(n+2)/(n!+(n+1)!+(n+2)!)=1/n!(n+2)=(n+1)/(n+2)!=(n+2-1)/(n+1)!=(n+2)/(n+2)!-1/(n+2)!
=1/(n+1)!-1/(n+2)!
所以，原式=1/2!-1/3!+1/3!-1/4!+省略+1/（n+1)!-1/(n+2)!
中间的全部抵消，只剩下首尾2项=1/2！-1/（n+2)!
这样就已经够简便，如果非要化成分数的话发比较烦=P(n+2)
n/(n+2)!