I"m doing a sequences difficulty where I need to write the an initial five terms of a sequence. It looks normal, however there is an exclamation note on the denominator:

$$a_n = frac1(n + 1)!$$

&

$$a_n = frac(-1)^nnn! + 1$$

What walk the exclamation mark mean, and also how carry out I go around this differently with the exclamation mark?




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The factorial that a number is represented by the exclamation suggest (!).The factorial the a number $x$ is often defined as the product of all positive integers less then or equal to $x$. For example:

$$4! = 4cdot3cdot2cdot1 = 24$$

It is often additionally useful to define $x!$ in a recursive relation:

$$x! = x(x-1)!$$

where $0! = 1$.

This method is often great because that helps describe why $0!=1$ (see additionally the "empty product" for more on this). Making use of the above explanation, we may find $4!$:

$$4! = 4(3)! = 4(3)(2)! = cdots = 4(3)(2)(1)(0)! = 4(3)(2)(1)(1) = 24$$


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edited Apr 9 "12 in ~ 1:29
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Michael hardy
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reply Apr 9 "12 at 0:09
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If the number is 4! climate you count down so it would certainly be $4 imes 3 imes 2 imes 1= 24$. Another thing is the if the number is 7! you would certainly count down till you gain to two. Therefore it would be $7 imes 6 imes 5 imes 3 imes 2 =5040$ 7 x 6 x 5 x 4 x 3 x 2 I just put in the 4 the was not listed although the prize is quiet 5040.


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edited Apr 27 "16 in ~ 2:46
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CommunityBot
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answered may 19 "14 at 23:03
HockeyloverHockeylover
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$endgroup$
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Hockeylover It's actually characterized recursively and also one "counts down" come $0! :=1$. $endgroup$
–user137731
january 7 "15 at 20:55


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