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
A sequence is a list of numbers, called terms, written in a specific order.
Explicit formulas define each term of a sequence using the position of the term. See
[link] ,
[link] , and
[link] .
An explicit formula for the
term of a sequence can be written by analyzing the pattern of several terms. See
[link] .
Recursive formulas define each term of a sequence using previous terms.
Recursive formulas must state the initial term, or terms, of a sequence.
A set of terms can be written by using a recursive formula. See
[link] and
[link] .
A factorial is a mathematical operation that can be defined recursively.
The factorial of
is the product of all integers from 1 to
See
[link] .
Questions & Answers
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4