I"m law a sequences problem where I need to write the very first five regards to 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 note mean, and also how do I go around this differently with the exclamation mark?

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

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

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

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

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

where \$0! = 1\$.

This an approach is often an excellent because it helps describe why \$0!=1\$ (see likewise the "empty product" for much more on this). Utilizing 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 in ~ 1:29

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

ArgonArgon
\$endgroup\$
2
0
\$egingroup\$
If the number is 4! then you count down so it would be \$4 imes 3 imes 2 imes 1= 24\$. One more thing is the if the number is 7! you would count down until you gain 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 simply put in the 4 the was not provided although the price is tho 5040.

re-publishing
mention
follow
edited Apr 27 "16 in ~ 2:46

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

Highly energetic question. Knife 10 call (not counting the combination bonus) in order come answer this question. The reputation requirement helps defend this concern from spam and non-answer activity.

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

Featured ~ above Meta
related
0
multiplying non-decreasing sequences
0
What go it median for a series to be convergent?
1
top top converging and also diverging sequences and their respective arithmetic median
1
What walk it mean for a duty to "preserve the borders of sequences"?
1
What walk this symbol typical in this context?
0
What go 2/(e^(-x)+1) mean?
2
What does \$(a_n)_n in A^yellowcomic.combbN\$ mean?
1
What go this definition of a succession mean?
1
What go it typical when a succession converges?
87
Why walk "Turn! Turn! Turn!" same 241217.524881?
warm Network inquiries more hot inquiries
inquiry feed

yellowcomic.com
company
stack Exchange Network
site architecture / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.4.40650

See more: What Does E Mean In Calculator ? What Does 3E11 Mean On A Calculator

yellowcomic.comematics ridge Exchange works ideal with JavaScript permitted