Summation of factorial sequence 1/2!+2/3!+3/4!+… +N / (n + 1)! What is it?

From K / (K + 1)! = (K + 1-1) / (K + 1)! = 1 / K! - 1 / (K + 1)!, it is concluded that
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)!

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