The formulas for some sequences include products of consecutive positive integers.
factorial , written as
is the product of the positive integers from 1 to
For example,
An example of formula containing a
factorial is
The sixth term of the sequence can be found by substituting 6 for
The factorial of any whole number
is
We can therefore also think of
as
Factorial
n factorial is a mathematical operation that can be defined using a recursive formula. The factorial of
denoted
is defined for a positive integer
as:
The special case
is defined as
Can factorials always be found using a calculator?
No. Factorials get large very quickly—faster than even exponential functions! When the output gets too large for the calculator, it will not be able to calculate the factorial.
Writing the terms of a sequence using factorials
Write the first five terms of the sequence defined by the explicit formula
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?