化简1/(2!)+2/(3!)+3/(4!)……(n-1)/(n!)

问题描述:

化简1/(2!)+2/(3!)+3/(4!)……(n-1)/(n!)

原式=[1/(2-1)!-1/(2!)]+[1/(3-1)!-1/3!]+……+[1/(n-1)!-1/n!]
=1/1!-1/2!+1/2!-1/3!+.+1/(n-1)!-1/n!
=1-1/n!
=(n!-1)/n!