Factorial Identities

Key Questions

  • What is a factorial?

    A factorial is a number multiplied by all of the integers below it.

    Eg, "Four factorial" #=4!##=4xx3xx2xx1=24#

    Mike G. · 1 · Apr 7 2015
  • What are factorials used for?

    Answer:

    Many things in various areas of mathematics.

    Explanation:

    Here are a few examples:

    Probability (Combinatorics)

    If a fair coin is tossed 10 times, what is the probability of exactly #6# heads?

    Answer: #(10!)/(6! 4! 2^10)#

    Series for sin, cos and exponential functions

    #sin(x) = x - x^3/(3!) + x^5/(5!) -x^7/(7!)+...#

    #cos(x) = 1 - x^2/(2!) + x^4/(4!) - x^6/(6!) +...#

    #e^x = 1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + ...#

    Taylor Series

    #f(x) = f(a)/(0!)+(f'(a))/(1!)(x-a)+(f''(a))/(2!)(x-a)^2+(f'''(a))/(3!)(x-a)^3+...#

    Binomial Expansion

    #(a+b)^n = ((n),(0))a^n + ((n),(1))a^(n-1)b + ((n),(2))a^(n-2)b^2 +...+((n),(n))b^n#

    where #((n),(k)) = (n!)/(k!(n-k)!)#

    George C. · 2 · Sep 6 2015
  • How do I find the factorial of a given number?

    The factorial of a number n is denoted as #n!#

    This is the product of all numbers from 1 to n.

    So we have #n! = n * (n - 1) * (n -2) * … * 2 * 1#

    So let us take #6!#

    #6! = 6 * 5 * 4 * 3 * 2 * 1#

    #6! = 720#

    Factorial Calculator

    Don S. · · Oct 1 2014

Questions

The Binomial Theorem