※ 引述《adamchi (adamchi)》之銘言：
: Sn=(3/1!+2!+3!)+(4/2!+3!+4!)+.....+(n+2)/(n!+(n+1)!+(n+2)!)=？
(n+2)/(n!+(n+1)!+(n+2)!)
=(n+2)/{n![1+(n+1)+(n+1)(n+2)]}
=(n+2)/[n!(n+2)^2]
=1/(n+2)n!=(n+1)/[(n+2)(n+1)n!]
=(n+1)/(n+2)!
原式=sigma(k+1)/(k+2)!=sigma[1/(k+1)! - 1/(k+2)!]=1/2 - 1/(n+2)!
k=1~n k=1~n
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.40.20.175