Factorization inside a factorial

[rmmstn]

This isn't really homework, just something that I encountered during an exercise and it got me thinking, is (2n)! the same as 2 * (n)! ?

 

[Deleted member 4993]

This isn't really homework, just something that I encountered during an exercise and it got me thinking, is (2n)! the same as 2 * (n)! ?

In general - NO - those expressions are not same. For example, assume n=3 - then

2n = 6 and (2n)! = 6! = 720

and 2 * (3!) = 12

I am sure you could have figured this out by yourself. Do that next time!

 

[skeeter]

[MATH](2n)! = 2n \cdot (2n-1) \cdot (2n-2) \cdot \, ... \, \cdot [2n-(n-1)] \cdot n \cdot (n-1) \cdot (n-2) \cdot \, ... \, \cdot [n - (n-1)][/MATH]

 

[Steven G]

(2n)! = 1*2*3...n*(n+1)...2n
2*n! = 2*1*2*3...*n