I"m doing a sequences problem where I need to write the first five regards to a sequence. The looks normal, yet there is one exclamation mark 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 an exclamation point mean in math

*

*

The factorial the a number is represented by the exclamation point (!).The factorial that a number $x$ is often described as the product of all hopeful integers much less then or equal to $x$. For example:

$$4! = 4cdot3cdot2cdot1 = 24$$

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

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

where $0! = 1$.

This technique is often great because that helps explain why $0!=1$ (see likewise the "empty product" for more on this). Using the above explanation, we may find $4!$:

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


re-superstructure
mention
follow
edited Apr 9 "12 at 1:29
*

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

ArgonArgon
23.8k99 gold badges8787 silver- badges127127 bronze badges
$endgroup$
2
add a comment |
0
$egingroup$
If the number is 4! climate you count under so it would be $4 imes 3 imes 2 imes 1= 24$. One more 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 the was not provided although the answer is still 5040.


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

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


include a comment |
Highly energetic question. Earn 10 call (not count the combination bonus) in order to answer this question. The reputation requirement helps safeguard this concern from spam and non-answer activity.

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


Featured top top Meta
associated
0
multiplying non-decreasing assignment
0
What go it median for a series to it is in convergent?
1
~ above converging and diverging sequences and also their particular arithmetic median
1
What does it mean for a role to "preserve the borders of sequences"?
1
What go this symbol typical in this context?
0
What go 2/(e^(-x)+1) mean?
2
What does $(a_n)_n in A^chrischona2015.orgbbN$ mean?
1
What walk this meaning of a sequence mean?
1
What does it average when a sequence converges?
87
Why walk "Turn! Turn! Turn!" same 241217.524881?
hot Network concerns much more hot questions
question feed
i ordered it to RSS
concern feed To subscribe to this RSS feed, copy and paste this URL into your RSS reader.


chrischona2015.org
agency
ridge Exchange Network
site design / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.21.40537




See more: How Many Inches Is 82 Cm Into Inches, How Many Inches Are 82 Centimeters

chrischona2015.orgematics stack Exchange works best with JavaScript allowed
*

your privacy

By click “Accept all cookies”, girlfriend agree ridge Exchange can store cookies on your an equipment and disclose details in accordance with our Cookie Policy.