证明:1/[(1+1)!]+2/[(2+1)!]+3/[(3+1)!]...n/[(n+1)!]=
问题描述:
证明:1/[(1+1)!]+2/[(2+1)!]+3/[(3+1)!]...n/[(n+1)!]=
接上面:=1-1/[(n+1)!]希望您能解答,越快越好
答
∵n/(n+1)!=1/n!-1/(n+1)!,
∴原式=1-1/2!+1/2!-1/3!+1/3!-1/4!+……+1/n!-1/(n+1)!
=1-1/(n+1)!.