I"m law a sequences problem where I need to write the very first five regards to a sequence. That looks normal, however there is one exclamation mark on the denominator:

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

&

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

What go the exclamation note mean, and also how do I go around this differently with the exclamation mark?




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

$$4! = 4cdot3cdot2cdot1 = 24$$

It is often likewise useful to describe $x!$ in a recursive relation:

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

where $0! = 1$.

This an approach is often an excellent because it helps describe why $0!=1$ (see likewise the "empty product" for much more on this). Utilizing the over explanation, us may discover $4!$:

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


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edited Apr 9 "12 in ~ 1:29
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Michael continuous
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answered Apr 9 "12 in ~ 0:09
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If the number is 4! then you count down so it would be $4 imes 3 imes 2 imes 1= 24$. One more thing is the if the number is 7! you would count down until you gain to two. So 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 simply put in the 4 the was not provided although the price is tho 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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Hockeylover It's actually identified recursively and one "counts down" to $0! :=1$. $endgroup$
–user137731
january 7 "15 at 20:55


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