急求数列求和题?2 3 4 99— ＋－ ＋ －＋...+ --- 100!
2020-04-29
急求数列求和题?
2 3 4 99
— ＋－ ＋ －＋...+ ---
100!
优质解答
(n-1)/n!=1/(n-1)!-1/n!
所以：2/3!+3/4!+...+99/100!
=(1/2!-1/3!)+(1/3!-1/4!)+...+(1/99!-1/100!)
=1/2!-1/100!
(n-1)/n!=1/(n-1)!-1/n!
所以：2/3!+3/4!+...+99/100!
=(1/2!-1/3!)+(1/3!-1/4!)+...+(1/99!-1/100!)
=1/2!-1/100!