求和1/2!+2/3!+3/4!+4/5!+……n/（n+1）!好像用裂项,为什么呢?
问题描述：
求和1/2!+2/3!+3/4!+4/5!+……n/（n+1）!好像用裂项,为什么呢?
答
原式=((1+1)/2!+(2+1)/3!+……(n+1)/（n+1)!)-(1/2!+1/3!+1/4!+.1/(n+1)!) =2/2!+3/3!+.(n+1)/(n+1)!-(1/2!+1/3!+1/4!+.1/(n+1)!) =(1/1!+1/2!+.+1/n!)-(1/2!+1/3!+1/4!+.1/(n+1)!) =1/1!-1/(n+1)...