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**[SOLVED] Seperating a Summation problem.**

## Homework Statement

The Problem:

Separate a sum into 2 pieces (part of a proof problem).

Using: [tex]X=

\sum^{n}_{k=1}\frac{n!}{(n-k)!}

[/tex]

Solve in relation to n and X:

[tex]

\sum^{n+1}_{k=1}\frac{(n+1)!}{(n+1-k)!}

[/tex]

## Homework Equations

???

## The Attempt at a Solution

[tex]

\sum^{n}_{k=1}[\frac{(n+1)!}{(n+1-k)!}]+\frac{(n+1)!}{(n+1-[n+1])!}

[/tex]

[tex]

\sum^{n}_{k=1}[\frac{(n)!}{(n-k)!}*\frac{(n+1)}{(n+1-k)}]+\frac{(n+1)!}{(n+1-[n+1])!}

[/tex]

[tex]

(n+1)*\sum^{n}_{k=1}[\frac{(n)!}{(n-k)!}*\frac{1}{(n+1-k)}]+(n+1)!}

[/tex]

I think this is fairly close but, I have no way of getting rid of the 1/(n+1-k) term.