Introduction of Factorial and Factorial Formula and Recurrence Relation (Especially for GATE-Geospatial 2022)

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Definition of Factorial

In Maths, the factorial of a positive integer is defined as the product of all the positive integers which are less than or equal to that given number. The product of some number and all the positive numbers less than that is known as the factorial.

The factorial of n indicates the multiplication of series of positive integers starting from n and descending till one.

The factorial is denoted by โ€œ!โ€ and sometimes .

Formula

In mathematics, the factorial of a natural number is the product of the positive integers less than or equal to . In short, a function that is equal to the first numbers multiplied together. This is written as and pronounced โ€˜ factorialโ€™ . If is an integer greater than factorial is the product of,

There is a special case of factorial of zero which is defined as equal to 1; i.e..

This means that there is one single permutation for zero objects, known empty or null set.

The factorial function formally defined by:

This Image Shows Factorial Formula

Where, is the product function which denotes the product of from 1 to .

For example,

This definition implies that

The number of ways one can choose k objects from among a given set of n objects, is given by so it called binomial coefficient,

.

The factorial function can also be denoted by the following recurrence relation:

Developed by: