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

kappa_am
Member
Registered: 2013-12-20
Posts: 55

### 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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,707

### 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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

kappa_am
Member
Registered: 2013-12-20
Posts: 55

### 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: 7,613

### 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

Children are not defined by school ...........The Fonz
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: 55

### 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: 7,613

### Re: need to develop a furmula for a string

It would help if you re-write the question.

Bob

Children are not defined by school ...........The Fonz
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: 55

### 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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