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#1 2010-02-09 09:03:14

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Sequences and Sums

I have much expanded my pages on Sequences, Series and Partial Sums.

The pages are:

- Sequences

- Sequences - Finding A Rule

- Sigma Notation

- Partial Sums

- Arithmetic Sequences and Sums.

- Geometric Sequences and Sums


Take your time reading them, and let me know what you think, any mistakes I may have made, any suggestions, etc.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2010-02-09 10:35:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Sequences and Sums

Hi MathsisFun;

In Sequences the phrase

"So it is best to say "A Rule" rather then "The Rule" (unless you have som" just trails off.

In Partial sums in the example of outer and inner bricks:

Feel free to reject this but with the change of indices k = i - 2

instead of k = 1. It doesn't change the sum but maybe you could mention that you dropped off the 0^2. If you think it won't complicate the explanation.

Good problem ( outer and inner bricks ) to illustrate the point.

In Geometric Sequences and Sums:

After this:

"    
Why "Geometric" Sequence?

Because it is like increasing the dimensions in geometry:"

I was a little disappointed that you didn't continue drawing r^4, r^5 ...

That was supposed to be funny!

Good, neat work! It is a lot of stuff so I may have missed something obvious but it looks good to me.


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 2010-02-09 10:49:46

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: Sequences and Sums

Sequences page is wonderful!
typos or browser:  In Notation:  there are two dots, not 3, to mean continue forever.
       In Many Rules: "more then one rule"
       In Many Rules: text cuts off: you have som (cuts off)
Still to review other pages...


igloo myrtilles fourmis

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#4 2010-02-09 21:20:16

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Sequences and Sums

Thanks guys, I will fix those. And any othe


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2010-02-10 03:37:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: Sequences and Sums

Hi MathsisFun;

Thanks guys, I will fix those. And any othe

Do you remember when you were a kid and you would make an ugly face. Your mother may have said not to do that because your face was going to stay that way?


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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#6 2010-02-10 08:27:41

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Sequences and Sums

bobbym wrote:

Your mother may have said not to do that because your face was going to stay that way?

I should have listened sad


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2010-02-10 08:43:22

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: Sequences and Sums

Sequences finding a rule is flawless as long as you want A Rule to have a capital A in 1st sentence after title.
I learned the n^2/2 rule, never heard of that for 2nd differences.  Was that just a guess?


igloo myrtilles fourmis

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#8 2010-02-10 10:14:13

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Sequences and Sums

Good point, I will fix the "a"s

n^2/2: yeah, I did kind of come up with that ... feel free to experiment with it and let me know what you find.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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