Factorial Identities
Factorial identities are fundamental mathematical expressions that relate to the products of consecutive positive integers. These identities play a crucial role in various branches of mathematics, particularly in combinatorics, calculus, and number theory. They offer powerful tools for simplifying expressions, solving equations, and establishing connections between different mathematical concepts. By understanding and utilizing factorial identities, mathematicians can efficiently manipulate expressions involving factorials, leading to elegant solutions and deeper insights into mathematical problems.
Questions
- How do you factor the trinomial #-5x^3+15x^2+20x#?
- How do you simplify #(9!)/(7!2!)#?
- The product of #(1-1/(2^2))*(1-1/(3^2))....(1-1/(9^2))*(1-1/(10^2))=a/b# then find a and b without full simplification?
- How do you simplify #(4!)!#?
- What is the constant term, in the expansion of #(x^3-2/(x^2))^10#?
- How do you write #60# using factorials?
- Use mathematical induction to prove that the statement is true for every positive integer n. Show your work.? 2 is a factor of n^2 - n + 2
- How do you simplify #((n+2)!)/((n-1)!)#?
- How do I find the factorial of a negative number?
- How do you solve #(n+2) ! = 132 n !#?
- How do you simplify the factorial expression #(25!)/(23!)#?
- How do you simplify #((n-1)!) /( n!) #?
- How do you solve #4^ { 2x } \cdot 4^ { 3} = 1#?
- How many zeros are there at the end of 100!?
- Prove that #1^99+2^99+3^99+4^99+5^99# is divisble by 5.?
- How can you simplify #1/(3sqrt(1-x^2/9))#?
- If 3^(x)-3^(x-1)=18 the value of 2^x is?
- How do you simplify #(15!)/(9!6!)+(7!)/(10!5!)#?
- Let #"*"# defined in #ZZ# by #p"*"q=p+q+3# for all #p,q in ZZ# Show that a) #"*"# is commutative in #ZZ#. b) identity element w.r.t #"*"# exists in #ZZ#?
- Find the following product: (5a+4)^3 ?