Im not sure what ! is called but my question is how is
(x+1)! / x! = (x+1)
also is there a formula to solve
(x+1)^a where a equals a # (for example 18)
In general is x is a real number with x>-1 [so that it isn't neccessarly an integer...] the factorial function [or 'Pi function' according to Gauss interpretation...] is defined as a definite integral that I don't report because the details are a little complex. If You want more details about it see...
Gamma function - Wikipedia, the free encyclopedia
In particular the 'facrorial function' satisfies the relation...
(1)
Till now we are 'all right'... a little less clear for Me is the second part of Your question, regarding the expression ... could You supply more details please?...
Kind regards
u can use : (sorry i do'nt know how this LaTex work just jet)
_____1_____
___1_2_1___
__1_3_3_1__
_1_4_6_4_1_
...................
for let's say 10th... it would be... 1_10_45_120_210_252_210_120_45_10_1
and u'll have
and so on.... but if u need to know let's sey n-th member of that u can use binomial template (or something... I'm bad with English... more or less)
well... when u do pyramid ... see that at each side are ones... but numbers inside are sum od two numbers from above...
look at 4... firs is one ... second is (above 1+3 =4) 4 .... 3rd is (above 3+3 =6) 6 ... 4th is (above 3+1=4) 4 and 5th is 1
and so on...
or like this :
or if u need let's say (k+1)th member u'll use this one :
that's one if u need (k+1)th member from begining ...
that's one if u need (k+1)th member from end ...
Pascal's triangle - Wikipedia, the free encyclopedia
Also for doing binomial coefficients you might find this useful
Combinations and Permutations Calculator
Choose No - No from dropdown menus, then for example n = 18 and r = 5 will give you the coefficient in front of the x^5 term of (x+1)^18 expanded. See
Binomial coefficient - Wikipedia, the free encyclopedia
o.O thanks but all those equations confused me but i did however found out how to do them Using Pascal's Triangle, thanks!
This is the way i figured it out:
X = pascal's number
n = n but as we move to the right we subtract 1
0 = 0 but as we move to the right we add 1
No its not, it is a function defined on the natural numbers. There is a way of extending it as you suggest (to a larger domain as well), but they are different things, and what you suggest here is useless to the poster of a question in the pre-university section of MHF
CB