Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

How do I prove

using Mathematica 9?

Is an inductive proof even possible in Mathematica?

*Last edited by ShivamS (2013-11-18 08:49:44)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Hi;

Mathematica already knows that is true but to do the steps

For the base case.

`1^2==(n*(n + 1) (2 n + 1))/6 /.n->1`

True

For the inductive step:

If that is true then

ought to be true. Subtract 1). from 2).

`((n*(n + 1) (2 n + 1))/6 /. n -> n + 1) - (n*(n + 1) (2 n + 1))/6 // FullSimplify`

(n+1)^2

The LHS is obviously (n+1)^2 so we are done.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

The first statement doesn't compute properly...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Hi;

Change the = to ==, I am sorry.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

Ok, thanks.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Hi;

I have made lots of changes to post #2.

Mathematica knows that sum:

`Sum[k^2, {k, 1, n}]`

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

`Sum[...,{i,1,n}]`

seems to be a bit faster than

`Sum[...,{i,n}]`

Why's that?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

I guess because he needs time to figure the lower index.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

But, it's an 0.03s difference.

*Last edited by anonimnystefy (2013-11-18 10:07:16)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

If it is not granularity, then that is probably the amount of time it would take.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

Granularity?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Trying to measure a very small increment with a large measuring stick produces granularity.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

How does that happen in M. Do you have an example?

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

I do not think I can. If you only have a 3 ft. stick and you and I both try to measure on inch, the measurements will vary greatly.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

I do not think that is the problem.

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Then I would go with the fact that it has to make one more decision.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,464

Thanks for fixing it.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,086

Hi;

You are welcome.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

Pages: **1**