How is factorial calculated? How to calculate factorial

If you list all of them, you'll see that after the reduction, all that's left is 1 divided by 2n (2n+1), and then n tends to infinity, so the denominator also tends to infinity, and then the equation is 0.

Obviously, (2n+1)!=1x2x3x…x(2n-1)x2nx(2n+1), and (2n-1)!=1x2x3x…x(2n-1), isn't it obvious that the reduction is only multiplied by 2n(2n+1)?

The concept of factorial].

Factorial is an operator notation invented by Christian Kramp (1760 1826) in 1808.

Factorial is also a term in mathematics.

This paragraph] [Calculation method of factorial].

Factorial is multiplication from 1 times 2 times 3 times 4 all the way up to the required number.

For example, if the required number is 4, then the factorial is 1 2 3 4, and the resulting product is 24, and 24 is the factorial of 4. For example, if the required number is 6, then the factorial is 1 2 3 ......6, the product obtained is 720, and 720 is the factorial of 6. For example, if the required number is n, then the factorial is 1 2 3 ......n, let the product be x, and x is the factorial of n.

This paragraph] [Factorial representation].

When expressing factorial, use "! to represent. For example, the factorial of x is denoted as x!

Such as: n!=n×(n-1)×(n-2)×(n-3)×.1

Another representation of factorial: (2n-1)!!

When n=2, 3!!=3×1=3

When n=3, 5!!=5×3×1=15

When n=4, 7!!=7×5×3×1=105

(and so on).

This paragraph] [factorial of numbers within 20].

The factorial numbers from 0 to 20 are listed below:

In addition, mathematicians define that 0! =1, so 0! =1！

This paragraph] [Definition range of factorial].

Usually what we call a factorial is defined in the range of natural numbers, and there is no factorial for decimals, like ! ，！

It's all wrong. However, sometimes we define a gamma function as a factorial of a non-integer because the value of the gamma function is a factorial of n-1 when x is a positive integer n.

Gamma function

x) = e (-t)*t (x-1)dt (the lower limit of the integral is zero, the upper limit is x>0,-1,-2,-3,......

Using the knowledge of integrals, we can prove (x) (x-1) *x-1).

So, when x is an integer n, (n) = (n-1)(n-2)......n-1)!

In this way, the gamma function actually extends the factorial.

Euler's equation. x!=)= -(ln(x)) ndx (the minimum limit of integration is zero, the upper limit is 1)(x>0).

Computer Science].

Use Ruby to find the factorial of 365.

def askfactorial(num) factorial=1;

1)return factorial end factorial=askfactorial(365)

puts factorial

Factorial formula].

n!~sqrt(2*pi*n)(n/e)^n

This formula is commonly used to calculate various limits related to factorials.

Factorial of 5. That's 5 4 3 2 1.

Factorial (a factorial of the number n is written as n!) Algorithm:

n!=1×2×3×..n-1)×n。

Definition: 0!=1，n!=(n-1)!×n

Factorial. Refers to multiplying from 1 times 2 times 3 times 4 all the way up to the required number.

If the required number is 4, then the factorial is 1 2 3 4, and the resulting product is 24, and 24 is the factorial of 4. For example, if the required number of bumpers is n, then the factorial is 1 2 3 ....Debate....Laughing and arguing n, let the product be x, and x is the factorial of n.

The main formula for factorial:

1. Any natural number greater than 1 n factorial representation: n!=1×2×3×……n or n!=n×(n-1)!

2. Double factorial of n: when n is an odd number, it means the product of all odd numbers not greater than n.

3. When n is an even number, it means the product of all even numbers not greater than n (except 0), such as 8!=2×4×6×8。

4. The factorial representation of the integer -n less than 0 is: (-n)!=1 / n+1)!

Expand and redefine.

For a long time, due to the unscientific definition of factorial, there are some difficulties in understanding after the expansion of factorial, and the problem of mathematical logic, the factorial has been extended from positive integers to complex numbers. The traditional definition is unclear. So it has to be scientifically redefined.

A truly rigorous factorial definition would be: for the number n, the product of all the same remainders whose absolute values are less than or equal to n is called the factorial of n, i.e., n!For the complex of this swift number should be the slow product of all the remainders of the same remainder of the modulo n less than or equal to n.

The canonical expression for any real number n is:

Positive number n=m+x, where m is the positive part and x is the decimal part.

Negative numbers n=-m-x, -m is the positive part, and -x is the decimal part.