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#1 2014-01-14 21:32:38

kappa_am
Member
Registered: 2013-12-20
Posts: 35

need to develop a furmula for a string

Hi all,
I have following string, and need to develop a single formula for all terms.
n, (n-1), (n-2)!,  (n-3)!+(n-4)!+(n-5)!+...(n-(n-1))!,   ((n-4)!+(n-5)!+(n-6)!+...(n-(n-1))!)+((n-5)!+(n-6)!+(n-7)!+...(n-(n-1))!)+...+(n-(n-1))!, ((n-5)!+(n-6)!+(n-7)!+...(n-(n-1))!)+((n-6)!+(n-7)!+(n-8)!+...(n-(n-1))!)+...+(n-(n-1))!

as illustrated after 3rd term, each sub-term (n-m)! in next term turn to (n-(m-1))!+ (n-(m-2))!+ (n-(m-3))!+....+(n-(n-1))!

any idea is appreciated

thank you:)

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#2 2014-01-14 22:02:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: need to develop a furmula for a string

Hi kappa_am;

A single formula? I am not following you. Can you explain a little better?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-01-14 23:45:38

kappa_am
Member
Registered: 2013-12-20
Posts: 35

Re: need to develop a furmula for a string

Hi,
lets put first two terms aside.
Doing so, I have a string of terms starts with (n-2)!. in this string each term is constructed according to the sub-terms of the previous term for example:
fist term is (n-2)! = (n-2)+(n-3)+(n-4)+(n-5)+...(n-(n-1)); the second term is (n-3)!+(n-4)!+(n-5)!+....+(n-(n-1))!
the third term will be summation of second side of the following equations:
in second term we have (n-3)! which is (n-3)+(n-4)+(n-5)...+(n-(n-1)) so one sub-term in third term is  (n-4)!+(n-5)!+(n-6)!+...(n-(n-1))!
in second term we have (n-4)! which is (n-4)+(n-5)+(n-6)...+(n-(n-1)) so another sub-term in third term is  (n-5)!+(n-6)!+(n-7)!+...(n-(n-1))!
...
in second term we have (n-(n-2)) which is (n-(n-2))+(n-(n-1)) so the last sub-term in third term is (n-(n-1))!
the other terms in this string are constructed as it is stated according to the previous term. I need a single formula that enables me to obtain each term.
an algorithm or a program in C language is also appreciated.

Thank you very much

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#4 2014-01-15 01:38:35

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: need to develop a furmula for a string

hi kappa_am

An exclamation mark (factorial) means the terms are multiplied.

eg 6! = 6 x 5 x 4 x 3 x 2 x 1

In post 3 you have put + not x.

fist term is (n-2)! = (n-2)+(n-3)+(n-4)+(n-5)+...(n-(n-1));

Which do you want?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2014-01-15 02:57:39

kappa_am
Member
Registered: 2013-12-20
Posts: 35

Re: need to develop a furmula for a string

Sorry,
I mean summation, not multiplication.

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#6 2014-01-15 20:47:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: need to develop a furmula for a string

It would help if you re-write the question.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2014-01-16 01:46:35

kappa_am
Member
Registered: 2013-12-20
Posts: 35

Re: need to develop a furmula for a string

I have a string of terms starts with ∑(n-m) {down limit of summation is m=2 and upper limit is m=(n-1). in this string each term is constructed according to the sub-terms of the previous term for example:
fist term is ∑(n-2) = (n-2)+(n-3)+(n-4)+(n-5)+...(n-(n-1)); the second term is ∑(n-3)+∑(n-4)!+∑(n-5)+....+∑(n-(n-1))
the third term will be summation of second side of the following equations:
in second term we have ∑(n-3) which is (n-3)+(n-4)+(n-5)...+(n-(n-1)) so one sub-term in third term is  ∑(n-4)+∑(n-5)+∑(n-6)+...∑(n-(n-1))
in second term we have ∑(n-4) which is (n-4)+(n-5)+(n-6)...+(n-(n-1)) so another sub-term in third term is  ∑(n-5)+∑(n-6)+∑(n-7)+...∑(n-(n-1))
...
in second term we have (n-(n-2)) which is (n-(n-2))+(n-(n-1)) so the last sub-term in third term is ∑(n-(n-1))=1
the other terms in this string are constructed as it is stated according to the previous term. In above equations "∑" means summation of the term located front of it starting from indicated number to n-1. for example ∑(n-4)= (n-4)+(n-5)+(n-6)+....+(n-(n-1).

I need a single formula that enables me to obtain each term. an algorithm or a program in C language is also appreciated.

Thank you very much

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