I"m law a sequences difficulty where I have to write the an initial five terms of 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 mark mean, and also how do I go around this in different ways with the exclamation mark?

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The factorial of a number is stood for by the exclamation allude (!).The factorial of a number \$x\$ is often explained as the product that all optimistic integers much less then or equal to \$x\$. Because that example:

\$\$4! = 4cdot3cdot2cdot1 = 24\$\$

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

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

where \$0! = 1\$.

This technique is often good because the helps describe why \$0!=1\$ (see likewise the "empty product" for more on this). Making use of the over 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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answer Apr 9 "12 at 0:09

ArgonArgon
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If the number is 4! then you count under so it would certainly be \$4 imes 3 imes 2 imes 1= 24\$. An additional thing is that if the number is 7! you would certainly count down until you get 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 just put in the 4 the was not listed although the prize is still 5040.

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edited Apr 27 "16 at 2:46

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

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