求和1/2!+2/3!+3/4!+4/5!+……n/(n+1)!好像用裂项,为什么呢?
题目
求和1/2!+2/3!+3/4!+4/5!+……n/(n+1)!好像用裂项,为什么呢?
答案
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)...
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