I"m act a sequences problem where I need to write the first five regards to a sequence. The looks normal, but there is an exclamation mark on the denominator:

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

&

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

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

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

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

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

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

where \$0! = 1\$.

This an approach is often an excellent because the helps describe why \$0!=1\$ (see additionally the "empty product" for an ext on this). Using the over explanation, we may uncover \$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

Michael hardy
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answered Apr 9 "12 in ~ 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 that if the number is 7! you would certainly count down till you acquire to two. So it would certainly 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 that was not detailed although the prize is quiet 5040.

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edited Apr 27 "16 in ~ 2:46

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

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

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