Simplifying factorials

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Main Question or Discussion Point

How can ((n+1)^2(*n!))/((n+1)!*n^2) be simplified to (n+1)/n^2?

My own answer is (n+1)^2/n^2, but its apparently wrong
 

Answers and Replies

  • #2
Here's how:

[tex]
\frac{(n+1)^{2}\cdot n!}{(n+1)!\cdot n^{2}}
=
\frac{(n+1)^{2}\cdot n!}{(n)!\cdot(n+1) \cdot n^{2}}
=
\frac{(n+1)\cdot n!}{(n)! \cdot n^{2}}
=
\frac{(n+1)}{n^{2}}

[/tex]

All you had to do was expand the (n+1)! into (n+1)n!.

:)
 

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