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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

This hasn't really been discussed in my class, and I don't think it will anytime soon. Say an amount of girls, n, went to the cinema(or took an air-plane) and had to sit in chairs numbered 1, 3, 5 ... The number of girls isn't known, but the sum of their chair numbers is 144. If I knew the amount of girls, I'd find the sum using:

Using mathematica I found that the problem could be solved with the following equation:

Where S is the sum of all odd numbers up to the nth odd number. Simplifying, this gives me:

Obviously, by now I would be able to solve my original problem with ease:

So, here's my question:

How do I go from

to

?

A general approach would be highly appreciated! Also if I've understood something wrong, please correct me

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

The Beginning Of All Things To End.

The End Of All Things To Come.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Thanks alot luca-deltodesco!

I'm not sure if I understand why

edit: Aha! Arithmetic series

*Last edited by Patrick (2006-10-31 07:16:46)*

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

if you want a proof for the 0.5n(n+1) thing. then here it is

what i want to prove is that

S(1) by expanding the sum, is ofcourse 1.

so the formula holds for n = 1

assuming that the formula is true for any n, i need to prove that it is true for any n+1

which is the above formula. So ive now shown that the formula holds for n = 1, and for any (n+1), given that it works for S(n)

by process of induction, this means that any integer n, n>=1, the sum of all integers 1 to n, is equal to S(n), since S(1) works, with the last set of formulae, S(2) must also work, which means S(3) must then also work too, and so on

*Last edited by luca-deltodesco (2006-10-31 07:19:07)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

okay, that made it a bit clearer than wikipedia... Thank you very much!

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