Express n! using product notation?

Question

jim_thompson5910 · Answer

By definition

n! = n*(n-1)*(n-2)*...*5*4*3*2*1

for example,

7! = 7*6*5*4*3*2*1

Notice how I start with 7 and count down to 1 (multiplying each number)

anonymous · Answer

I understand that part, but what exactly is product notation?

jim_thompson5910 · Answer

product just means multiply

I guess you could represent it like this

$$\Large \prod_{k=1}^{n}k$$

which is a short hand for what I wrote above

geerky42 · Answer

You know summation ( $\sum$ ) ? 

Product notation is "multiplication version" of summation.

jim_thompson5910 · Answer

the big pi symbol is like the sigma symbol (which was used for sums) but it's used for products

anonymous · Answer

So they're asking for n! in that format?

anonymous · Answer

Oh, never mind. I get it, that is n! in product notation, right?

jim_thompson5910 · Answer

yes

$$\Large n! = \prod_{k=1}^{n}k$$

jim_thompson5910 · Answer

since 

$$\Large \prod_{k=1}^{n}k = 1*2*\cdots *(n-1)*n$$ 

and you can rearrange the factors