Sequence: determine if (n + 2)! / n! converges

[flakine]

If converge, find limit:

(n+2)!/n!

The answer is (n+2)(n+1), diverges. But how did they get the answer???

These types of problems are difficult to understand, can someone help?

 

[galactus]

I assume you know what a factorial is. Look at it this way:

\(\displaystyle \frac{(n+2)(n+1)n(n-1)(n-2)...........}{n(n-1)(n-2)............}\)

Cancel:

\(\displaystyle \frac{(n+2)(n+1)\sout{n}\sout{(n-1)}\sout{(n-2)}............}{\sout{n}\sout{(n-1)}\sout{(n-2)}.............}\)

That leaves you with:

\(\displaystyle (n+2)(n+1)\)