1. ## Sequences & Series

I have a simple question about sequence $an$.

$
an = \frac{(n+2)!}{n!}
$

I understand as n goes to infinity the denominator sequence looks like: { $1, 1 * 2, 1 * 2 * 3, ...$}

But what does it do with $(n+2)!$ ?

2. All I wanna know is what $(n + 2)!$ is when you plug say 1, 2, and 3 in for $n$.

If anyone knows, throw me a reply cause I'm lost. (I'm not familiar with the exclamation mark notation.)

3. ! = Factorial from what I remember it means...

4! = 1x2x3x4 = 24 etc....

3! = 1x2x3 = 6 etc...

4. Originally Posted by justinwager
! = Factorial from what I remember it means...

4! = 1x2x3x4 = 24 etc....

3! = 1x2x3 = 6 etc...

Awesome! Thank you. :]

5. Originally Posted by freyrkessenin
I have a simple question about sequence $an$.

$
an = \frac{(n+2)!}{n!}
$

I understand as n goes to infinity the denominator sequence looks like: { $1, 1 * 2, 1 * 2 * 3, ...$}

But what does it do with $(n+2)!$ ?
Note that $(n+2)!=(n+2)(n+1)n!$

So $a_n=\frac{(n+2)(n+1){\color{red}n!}}{{\color{red}n !}}=\dots$

--Chris

6. Originally Posted by freyrkessenin
I have a simple question about sequence $an$.

$
an = \frac{(n+2)!}{n!}
$

I understand as n goes to infinity the denominator sequence looks like: { $1, 1 * 2, 1 * 2 * 3, ...$}

But what does it do with $(n+2)!$ ?
So you know that:

$n!=1 \times 2 \times 3 \times ... \times (n-1) \times n$

Then you also know that:

$(n+2)!=1 \times 2 \times 3 \times ... \times (n-1) \times n \times (n+1) \times (n+2)$

and so after cancelling tha common terms:

$
a_n = \frac{(n+2)!}{n!}=(n+1)(n+2)
$

$n!$ is the factorial of $n$ and defined as above.

RonL