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## Homework Statement

Prove that 1/2 P(2,1) + 2/3 P(3,2)+3/4 P(4,3)+ ... + n/(n+1) P(n+1,n) = (n+1)! - 1

Please help!

## Homework Equations

P(n,r) = n!/(n-r)!

## The Attempt at a Solution

The inequation can be simplified to:

1*1! + 2*2! + 3*3!+ ... + n*n! = (n+1)! - 1 (*)

Use the induction method:

1/Base case: n=1 -> 1=1 true

2/Inductive case: suppose (*) is true

Need to prove: 1*1! + 2*2! + 3*3!+ ... + (n+1)*(n+1)! = (n+2)! -1