Question

What is the factorial of \[(n + 1)?\]

Answer 1

Hint: The factorial of various is the feature that multiplies the number by means of each natural wide variety below it. Hence the concept \[n!(n + 1)\] is used in reducing the answer. The concept of factorial is used in permutations and combinations.

Complete step-by-step solution:
Since we know that factorial or \[(n!)\] is the product of all numbers less than that up till \[1\]. To get a factorial we have to multiply \[n\] with the next number. Hence we use the concept of \[(n + 1).n!\] Factorial of a whole range \[n\] is defined because it is manufactured from that range with each complete variety until we get a \[1\].
Hence, we find that that the factorial of \[n + 1\] is
\[(n + 1)! = (n + 1).n.(n - 1).(n - 2)...3.2.1\]
Additional Information: The study of factorials is at the primary part of several subjects in mathematics, together with the wide variety of concepts, algebra, geometry, probability, data, graph concept, and discrete arithmetic, etc. The factorial of a number of is the feature that multiplies the quantity via every natural quantity underneath it. Symbolically, factorial may be represented as "\[!\]" So, \[n\] factorial is made of the first \[n\] natural numbers and is represented as \[n!\] Using the method for factorials we are able to easily derive what's moreover, the definition of the \[0\] factorial includes the simplest one permutation of \[0\] or no items. Ultimately, the definition also validates some of the identities in combinatorics.

Note: One location wherein factorials are usually used is in permutations & mixtures. The factorial function is described for all fine integers, together with 0. Further, in which n = zero, the definition of its factorial (n!) encompasses the product of no numbers, which means that it is equal to the multiplicative identification in broader phrases. The use of factorials is widely done in Permutation and Combination.