Math Is Fun Forum

kappa_am

Member

Registered: 2013-12-20

Posts: 63

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:)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
Always satisfy the Prime Directive of getting the right answer above all else.

kappa_am

Member

Registered: 2013-12-20

Posts: 63

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

kappa_am

Member

Registered: 2013-12-20

Posts: 63

Re: need to develop a furmula for a string

Sorry,
I mean summation, not multiplication.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

kappa_am

Member

Registered: 2013-12-20

Posts: 63

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