I"m law a sequences trouble where I need to write the very first five terms of a sequence. It looks normal, yet there is an exclamation note on the denominator:

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

&

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

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

You are watching: What does exclamation point mean in math

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

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

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

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

where $0! = 1$.

This method is often great because that helps define why $0!=1$ (see likewise the "empty product" for much more on this). Using the above explanation, we 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 at 1:29

Michael hardy
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answered Apr 9 "12 in ~ 0:09

ArgonArgon
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If the number is 4! climate you count down so it would be $4\times 3 \times 2\times 1= 24$. Another thing is that if the number is 7! you would count down till you acquire to two. So 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 the was not listed although the price is quiet 5040.

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edited Apr 27 "16 at 2:46

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answered may 19 "14 in ~ 23:03
HockeyloverHockeylover
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Hockeylover It's actually defined recursively and also one "counts down" come $0! :=1$. $\endgroup$
–user137731
january 7 "15 in ~ 20:55

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## Not the prize you're spring for? Browse various other questions tagged calculus real-analysis sequences-and-series notation factorial or questioning your own question.

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