Math Is Fun Forum

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Convert sum into equation

I have a sum:

How to rewrite it without sum sign and i? In other words, I need to see it in f(N) form.

Last edited by White_Owl (2010-09-28 09:15:57)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Convert sum into equation

Hi;

---

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.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Convert sum into equation

Ok... How did you do it?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Convert sum into equation

Hi;

Since you did not ask for the method. I just had a computer do it for me.

There are many methods to do that problem.

The first is the summation calculus, as there is an integral calculus there is a summation calculus. Sums are the discrete counterpart to the continuous integrals you already know. It is a big field at least as large as integral calculus and much less well known.

The second is using the Euler Mclaurin summation formula. This formula relates integrals, sums and derivatives.

Third, curve fitting and then using induction.

Fourth is using a table.

---

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.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Convert sum into equation

Since I do not understand your answer, the next question would be: "What books should I read?"

And what program do you use for this formula conversion?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Convert sum into equation

Hi White_Owl;

What are you currently studying, and why are facing questions like that sum? This will give me an idea as to how to proceed.

---

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.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Convert sum into equation

I am in Algorithm Analysis class right now.
I managed to convert the set of loops into the sum form, but stuck after it...
I have Rosen's Discreet Math book but can not find there any clues on this particular formula conversion.

I have very extensive practical computer programming background, but know I am trying to study the theoretical approach to computer science. Hence the strange questions...
My calculus days was more 20 years ago and stuff like integrals and derivatives - I know what it is about but can not calculate them on paper even if it kills me.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Convert sum into equation

I managed to convert the set of loops into the sum form, but stuck after it...

I understand completely. My first tip is this: Since you are a computer sort of problem solver, never, ever, reduce a problem to something in terms of something you can not deal with. Rather try to reduce it to things you can deal with.

Be that as it may. First I use these two books very heavily. I am very computer oriented too.

1) Calculus of finite differences and difference equations - Murray Spiegel, it is a schaums book.

2) Numerical Analysis ( a must for serious computer work ) Francis Scheid also a schaums book.

From them you will learn the summation calculus and difference equations. Sums like that will be easy for you then.

3) Get your hands on one of these. Mathematica, Maple, Mupad, Maxima, Derive, Sage etc.

I will gladly go over each of the 4 methods I have stated above, if you have the time and the patience.

---

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.