sandy.bridge said:so (2n)!=(2*1)*(4*3*2*1)*(6*5*4*3*2*1)*...*(2n*(2n-1)*...*1). This can be taken a step further, though correct?
That's more like it!sandy.bridge said:(2n)!=(2n*(2n-1)*(2n-2)*...*1) ?
sandy.bridge said:Okay. How exactly does that end up being: 1*2*3*...*n*(n+1)*(n+2)*(n+3)*...*(2n) ?
sandy.bridge said:(2n)!=(2n*(2n-1)*(2n-2)*...*1) ?
sandy.bridge said:Okay. How exactly does that end up being: 1*2*3*...*n*(n+1)*(n+2)*(n+3)*...*(2n) ?
For some reason I was having a hard time seeing from n+1 to 2n. I completely see it now. Thanks!SteamKing said:Look at counting to 2n this way:
1,2,3,4,...,n-2,n-1,n - the sequence of all integers from 1 to n
n+1,n+2,n+3,..., n+n-2,n+n-1,n+n - the sequence of integers from n+1 to 2n
A factorial is a mathematical operation denoted by an exclamation mark (!) that represents the product of all positive integers from 1 up to a given number. For example, 4! (read as "four factorial") is equal to 1 x 2 x 3 x 4 = 24.
To calculate a factorial, you simply multiply all positive integers from 1 up to the given number. For example, to calculate 5!, you would do 1 x 2 x 3 x 4 x 5 = 120. You can also use a calculator or a factorial function in programming languages to calculate factorials.
Multiplying by an integer in factorials allows us to find the factorial of numbers that are not necessarily integers. For example, if we want to find 4.5!, we can multiply 4.5 by 3.5 (since 3.5 is the integer value before 4.5) to get 15.75. This allows us to extend the concept of factorials to non-integer numbers.
No, factorials are only defined for positive integers. Multiplying negative numbers in factorials would not make mathematical sense and would result in an undefined answer.
The largest factorial that can be calculated depends on the limitations of the computer or calculator being used. However, as the factorial operation involves multiplying increasingly larger numbers, the calculated value can quickly become too large to be represented accurately in most systems.