The symbol n! (pronounced: n-faculty) is defined as an abbreviated notation for the product of the natural numbers from 1 to n – math homework solver . Combinatorial formulae in particular can be expressed in rational form using the factorial notation.
For the product of the natural numbers from 1 to n, the abbreviated notation is the symbol n! (pronounced: n-faculty) is used as an abbreviated notation, i.e.:
The factorial notation is defined inductively. One generally starts from the definition
0 !=1 (or 1 !=1)
and then defines:
(n+1) !=n !⋅(n+1)
The following table gives the values for (the function) n! up to n = 10 (which can also be called up directly by means of a special key on most calculators):
You can see that the values for n! grow very quickly as n gets larger. For example, a pocket calculator for n = 69 gives the value 1.711 224 524⋅10^98. Values for larger n are generally no longer shown by a pocket calculator with a ten-digit display – geometry homework help . However, they can be determined step by step on the basis of the above recursive definition.
The factorial notation is used, among other things, in combinatorics for number determination (permutations) and especially for the definition of binomial coefficients.
The function n! – do my homework – can be called up directly by means of a special key on most pocket calculators directly by means of a special key.
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