What is the value of \[\left( n! \right)\] by formula?

Hint: Problems like these are quite straight forward and are easy to solve once we understand the underlying concepts behind the question. For these types of questions, we need to have some basic as well as to some extent, advanced knowledge of factorials, fractions and the number systems. The first thing that we need to be aware of is the formula of the factorial of any number ‘n’. We need to remember that the factorial of any number ‘n’ is represented by \[\left( n! \right)\] . According to the formula, the factorial of any number is the product of consecutive integers numbers from \[1\] to \[n\] . We need to represent this formula mathematically.

Complete step-by-step answer:
Now we start off with the solution to the given problem by writing that the general basic formula for the factorial of any number \[n\] is the product of consecutive integers starting from \[1\] and going all the way up to ‘n’. Representing this theoretical statement mathematically, we get, the factorial of the number ‘n’ is given by,
\[n!=1.2.3.4.5......n\]
So this is the answer to our problem. This formula is applicable for any positive integers starting from \[1\] . We need to remember that the value of \[0!\] is equal to \[1\] .

Note: For problems like these we need to have a thorough understanding of the chapters like number systems, fractions and factorial. One very important thing to note down here in this problem is that, factorial is not defined for negative numbers. It is only defined for positive integers and \[0\] . We should also keep in mind that the value of \[0!\] is equal to \[1\] .