Should I Patent This?

[Jacob Roman]

Well I'm starting college again August 23rd. And I need to take Calculus 1 as one of my prerequisites to graduate, but couldn't cause they want me to take Pre-Calculus prior to taking Calculus. So I started learning on my own prior to taking the class some Pre-Calculus. Mostly while sitting on the toilet as reading material. Ok maybe that was TMI

So I run into Summation. Yes that funky looking greek letter thats shaped like an E (called a sigma Σ) that involves adding in increments from a starting point to an ending point. For example, if i = 1, and n = 5, the summation would be 1 + 2 + 3 + 4 + 5 = 15. It's literally almost just like a For loop in programming. And I was playing around with em. They gave a formula to solve summations not just in the book, but also on the internet, and so far its the only formula given:

n
Σ
i = 1

=

n(n + 1)
---------
2

However there is just one problem. The formula offered is only limited to Summations that start at 1. How would you solve other summations such as starting at 3 or 5 or any other number. So I tried finding a pattern for simple summations and found it. The new formula I came up with was missing a chunk from the one offered in math books and online:

n(n + 1) - i(i - 1)
--------------------
2

So now you can put in whatever starting position you want for i, and ending position for n, and it'll solve the summation. Everything works so far. Question is, has this already been found or did I find a new way to solve Summations and should patent it right away?

[boops boops]

Well I'm starting college again August 23rd. And I need to take Calculus 1 as one of my prerequisites to graduate, but couldn't cause they want me to take Pre-Calculus prior to taking Calculus. So I started learning on my own prior to taking the class some Pre-Calculus. Mostly while sitting on the toilet as reading material. Ok maybe that was TMI

So I run into Summation. Yes that funky looking greek letter thats shaped like an E (called a sigma Σ) that involves adding in increments from a starting point to an ending point. For example, if i = 1, and n = 5, the summation would be 1 + 2 + 3 + 4 + 5 = 15. It's literally almost just like a For loop in programming. And I was playing around with em. They gave a formula to solve summations not just in the book, but also on the internet, and so far its the only formula given:

n
Σ
i = 1

=

n(n + 1)
---------
2

However there is just one problem. The formula offered is only limited to Summations that start at 1. How would you solve other summations such as starting at 3 or 5 or any other number. So I tried finding a pattern for simple summations and found it. The new formula I came up with was missing a chunk from the one offered in math books and online:

n(n + 1) - i(i - 1)
--------------------
2

So now you can put in whatever starting position you want for i, and ending position for n, and it'll solve the summation. Everything works so far. Question is, has this already been found or did I find a new way to solve Summations and should patent it right away?

Your summation formula is incomplete because the term to be summed isn't shown. The most complete way to write it would be:

i = n
Σ i
i = 0

But you can omit the "i=" because this would also be understood:

n
Σ i
0

It isn't quite the same as a loop in VB.Net because the counting variable i can't exist outside the calculation. So i can't appear in the formula for the resulting sum. Your "discovery" is actually correct except that your use of the symbol i is wrong. You should write the summation of all integers from m to n inclusive like this:

n
Σ i
m

and the formula for the sum will be:

n(n + 1) - m(m - 1)
--------------------
2

As to the patent, I think you should write to Microsoft's legal department about that. They may want to charge you royalties for using it.

By the way, consider putting questions like this on the Maths forum, because you'll get the scrutiny of some math heavyweights there. And it's a bit too quiet there.

BB

[Nightwalker83]

Just make sure that your idea hasn't actually been done before by someone else.

[Jacob Roman]

Ill need to research it more to see if it exists. It would be pretty awesome to be the inventor of a new math method

[TysonLPrice]

I didn't realize you could patent math. Who should all those kids be paying for 1 + 1 = 2?

[passel]

You should probably read beyond the first chapter of the book.
A quick look at "Summation" in Wikipedia shows one series which should look quite familiar to you.

[Jacob Roman]

Rats

There goes my chance of being famous.

[TysonLPrice]

You should probably read beyond the first chapter of the book.
A quick look at "Summation" in Wikipedia shows one series which should look quite familiar to you.

What book are you referring too? I'm sure that Wikipedia article is interesting but I don't speak spanish...

[passel]

What book are you referring too? I'm sure that Wikipedia article is interesting but I don't speak spanish...

I was making an inference to whatever book Jacob is reading.

As for the Wikipedia page, I did a google search on the word "summation", and the first hit was the english wikipedia page, http://en.wikipedia.org/wiki/Summation.
(If you don't speak Spanish, you probably shouldn't be looking at the Spanish version of Wikipedia ).

Now, I am not any kind of math wiz (high school education, and not a good one, and Navy Technical schools (good)), so don't know or care about most of this, but there are quite a few summation series described on that page.

The excerpt I posted was the fourth summation under the section:
Some summations of polynomial expressions