I"m doing a sequences difficulty where I have to write the first five terms of a sequence. That looks normal, but there is an exclamation mark on the denominator:

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

&

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

What walk the exclamation mark mean, and how carry out I go about this in different way with the exclamation mark?




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

$$4! = 4\cdot3\cdot2\cdot1 = 24$$

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

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

where $0! = 1$.

This method is often good because that helps define why $0!=1$ (see likewise the "empty product" for an ext on this). Making use of the over explanation, us 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 at 1:29
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Michael hardy
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answered Apr 9 "12 at 0:09
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If the number is 4! then you count down so it would certainly be $4\times 3 \times 2\times 1= 24$. Another thing is the if the number is 7! you would certainly count down until you acquire to two. Therefore it would be $7\times 6\times 5\times 3\times 2 =5040$ 7 x 6 x 5 x 4 x 3 x 2 I simply put in the 4 that was not detailed although the price is still 5040.


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


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