证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!

来源：学生作业帮助网编辑：六六作业网时间：2024/05/16 18:06:32

证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!证明1/2!+2/3!+3/4!+.+n/(n+

证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!

证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
所以左边=1/1!-1/2!+1/2!-1/3!+……+1/n!-1/(n+1)!
=1-1/(n+1)!

n/(n+1)!=1/n!-1/(n+1)!
每个式子这样分解，加起来就行了