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
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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