What do you think?

bobbym · 2011-03-16 21:27:16

Hi phrontister;

The next time that should occur and you are stuck for the formula of the average of {1,2,3,...,n}. Just do this:

Sum[k,{k,1,n}] / n and Math will spit out (n+1)/2

phrontister · 2011-03-16 21:31:55

So it did! Didn't know that. Ta.

gAr · 2011-03-16 21:38:19

Hi bobbym and phrontister,

Sorry for interrupting.

Bobbym,

Ya, I saw that. I actually meant how you solved using experimental math.
I too observed a pattern like:

where P_k is the product to k terms, and n_1, n_2 ... are the numerators of a_1, a_2 ...

And for the average, I found your way:

bobbym · 2011-03-16 21:47:36

Hi all;

Presently I trying to stuff my face with some soup which I will have make first. Please hold!

gAr · 2011-03-16 21:53:44

Ok, sorry!

bobbym · 2011-03-16 22:48:08

Hi gAr;

Do not be. That soup was awful. Sorry for the delay.

Do you have an Integer relation command in Sage? Or a PSLQ?

gAr · 2011-03-16 23:02:36

Hi bobbym,

That soup was awful.

Sorry to hear that!

I don't know about PSLQ, it may be available in sympy.
But why did you ask? Did you use it to solve the product?

bobbym · 2011-03-16 23:18:38

Yes, it is the cornerstone of experimental math. That is okay Mathematica does not have a PSLQ either, I had to write it. Maple has one.

We have spoken of Ramanujan. In a sense he is the author of the whole idea.

Here is what you do, using any package that you are comfortable with.

1) Form a table of a(1) to a(100) from that recurrence to 100 digits for each one.

2) Multiply all the entries. Call the value A.

1) Form a table of a(1) to a(200) from that recurrence to 100 digits for each one.

2) Multiply all the entries. Call the value B.

Compare A and B and keep the digits that are the same. Stop at the first digit that is not.

Post your answer here.

gAr · 2011-03-16 23:34:17

Oh, I see.
Doesn't that take a long time?
How can I use PSLQ? PSLQ's implemented in mpmath.

bobbym · 2011-03-16 23:43:38

Hi gAr;

Just product all the numbers. For example:

{1,2,3,4,5,6} = 1*2*3*4*5*6 = 720. You will have 100 of them to do and then 200. Your language should support some command that multiplies all the elements of an array or a vector. I think python does.

When you have the value we can go on to how to use a PSLQ.

gAr · 2011-03-16 23:54:29

Hi bobbym,

I'll check.
Thanks for introducing me to experimental math, looks interesting!
When posting the answer I thought you too solved the problem similar to the way I solved.

bobbym · 2011-03-17 00:01:57

I wished I had but the truth is I made some mistakes and could not get your idea to work. This is just going to show another way to get the answer you got but it is not as rigorous.

gAr · 2011-03-17 00:09:59

Okay.
I have enjoyed attempting all the questions you have posted. I'm curious to know how you imagine the questions so fast. Are the questions in your notebooks from the past?

bobbym · 2011-03-17 00:23:28

They almost always are problems that I am currently working on and have solved. If I am posting somewhere and I think the problem is interesting I will bring it over here.

I am proud to say that I have had Jane, mathsyperson, JimmyR, ElainaVW, phrontister, Fruityloop, Howard and yourself answer questions on this thread. It has been a real honor to watch how you all work.

gAr · 2011-03-17 00:36:00

That's cool!

Yes, I too have seen their work, and they all have solved in amazing ways. I wish them to be back to the forum.

bobbym · 2011-03-17 00:43:42

Me too. People have other lives and get pulled apart over time.

gAr · 2011-03-17 00:53:15

Yes, I understand it.
I wish to have a career in mathematics, which doesn't include lecturing!

bobbym · 2011-03-17 00:55:31

Hi gAr;

What kind of math do you like most and why no lecturing?

gAr · 2011-03-17 01:03:25

Hi bobbym,

I guess I like applied math, and may be computational math too. I like a job where there's less talking and more thinking.

bobbym · 2011-03-17 01:09:02

I like applied math and computational is my favorite. Teaching is not everyone's dream. I wish you all the success that you can get. If you want my opinion I believe you will achieve your goal.

gAr · 2011-03-17 01:20:52

Thank you for your good wish.
People give too much importance to the degree, and mine doesn't belong to mathematics.
Anyway, I too hope for the good. Just looking at mathematical symbols lightens up my mind

bobbym · 2011-03-17 01:28:18

Yes, my brother is like that. He is a much better than I am. Only he does not like forums at all so I cannot get him to post alot.

I agree about degrees but I am the only one. Mathematics is a beautiful study but I am not always happy with those who do it.

gAr · 2011-03-17 01:38:41

Oh, is it? I prefer written communication to oral, we can always read again if we don't understand at once. Asking people to repeat doesn't look so polite

And yes, some colleagues are an occupational hazard!

bobbym · 2011-03-17 01:44:38

And yes, some colleagues are an occupational hazard!

Agreed!

gAr · 2011-03-17 03:23:55

Hi bobbym,

Looks like some powerful algorithms are implemented in mpmath.
Check these if you haven't already: http://mpmath.googlecode.com/svn/trunk/doc/build/identification.html

Math Is Fun Forum

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