求和1/2!+2/3!+3/4!+……n/(n+1)!

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求和1/2!+2/3!+3/4!+……n/(n+1)!求和1/2!+2/3!+3/4!+……n/(n+1)!求和1/2!+2/3!+3/4!+……n/(n+1)!1/2!+2/3!+3/4!+……n/

求和1/2!+2/3!+3/4!+……n/(n+1)!
求和1/2!+2/3!+3/4!+……n/(n+1)!

求和1/2!+2/3!+3/4!+……n/(n+1)!
1/2!+2/3!+3/4!+……n/(n+1)!
=(1/1-1/2!)+(1/2!-1/3!)+(1/3!-1/4!)+...+[1/n!-1/(n+1)!]
=1-1/(n+1)!

与自然对数有关。

n/(n+1)! =[(n+1)-1]/(n+1)!=1/n! - 1/(n+1)!
1/2!+2/3!+3/4!+……+n/(n+1)!
=(1/1!-1/2!)+(1/2! -1/3!)+……+[1/n! - 1/(n+1)!]
=1/1! -1/(n+1)!
=1-1/(n+1)!