I"m doing a sequences problem where I need to write the very first five regards to a sequence. The looks normal, but 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 also how perform I go around this in different way with the exclamation mark?

You are watching: What does a exclamation mark mean in math

The factorial that a number is represented by the exclamation point (!).The factorial of a number $x$ is often explained as the product that all optimistic integers much less then or same to $x$. Because that 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 the helps define why $0!=1$ (see likewise the "empty product" for more on this). Using the over explanation, us may discover $4!$:

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

re-publishing
mention
monitor
edited Apr 9 "12 at 1:29

Michael hardy
1
answer Apr 9 "12 in ~ 0:09

ArgonArgon
$\endgroup$
2
0
$\begingroup$
If the number is 4! climate 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 count down till you get to two. Therefore it would certainly be $7\times 6\times 5\times 3\times 2 =5040$ 7 x 6 x 5 x 4 x 3 x 2 I just put in the 4 that was not listed although the prize is tho 5040.

re-publishing
point out
monitor
edited Apr 27 "16 at 2:46

Community♦
1
answered may 19 "14 in ~ 23:03
HockeyloverHockeylover
1
$\endgroup$
2
$\begingroup$
Hockeylover It's actually characterized recursively and one "counts down" to $0! :=1$. $\endgroup$
–user137731
january 7 "15 at 20:55

Highly active question. Earn 10 call (not counting the association bonus) in order come answer this question. The reputation requirement helps protect this question from spam and also non-answer activity.

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

Featured top top Meta
related
0
multiplying non-decreasing sequences
0
What does it average for a series to it is in convergent?
1
top top converging and diverging sequences and also their respective arithmetic average
1
What does it typical for a function to "preserve the borders of sequences"?
1
What walk this symbol typical in this context?
0
What walk 2/(e^(-x)+1) mean?
2
What does $(a_n)_n \in A^\civicpride-kusatsu.netbbN$ mean?
1
What walk this an interpretation of a sequence mean?
1
What go it average when a succession converges?
86
Why walk "Turn! Turn! Turn!" same 241217.524881?
warm Network inquiries much more hot questions
concern feed

civicpride-kusatsu.netematics
company
stack Exchange Network
site style / logo © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.9.21.40262

See more: How To Unlock Luigi In Smash Ultimate, How To Unlock Luigi In Super Smash Bros

civicpride-kusatsu.netematics ridge Exchange works finest with JavaScript enabled