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Can someone do a proof for this problem... *MATH GENIUSES*

C

chiwawa626

Lifer
The problem is proving that the sum of n*n! from i=1 to n is equal to (n+1)!-1

To get an idea of what i mean here is the proof from Dr Math, but its proved through induction:
http://mathforum.org/library/drmath/view/56044.html

I understand how it works through induction, but induction dosent really explain why it works, can someone do a regular proof for this problem?

thanks 🙂
 
Originally posted by: notfred
proof by induction is about the most useless thing they mke you do in school.
Click to expand...

oh come on, it makes you think in ways that are beneficial to in RL. Not everything in school can be applied directly ya know.
 
Originally posted by: notfred
proof by induction is about the most useless thing they mke you do in school.
Click to expand...

umm yeah, except it proves about 90% of the fundamental theorems of algebra.

-silver
 
Originally posted by: chiwawa626
Originally posted by: MercenaryForHire
Do your own homework. 😛

- M4H
Click to expand...

My homework is proof by induction, which i understand, but i dont really know why it works.
Click to expand...

you don't understand how this proof works or induction in general?
 
Originally posted by: agnitrate
Originally posted by: notfred
proof by induction is about the most useless thing they mke you do in school.
Click to expand...

umm yeah, except it proves about 90% of the fundamental theorems of algebra.

-silver
Click to expand...

I also figured as a computer scientist (at least I think Notfred has or is pursuing a CS major) he would understand the importance of induction. Sure, it may not be directly applicable to some of the things he does directly when programming, but it is fundamentally very important.


 
Originally posted by: fivespeed5
Originally posted by: chiwawa626
Originally posted by: MercenaryForHire
Do your own homework. 😛

- M4H
Click to expand...

My homework is proof by induction, which i understand, but i dont really know why it works.
Click to expand...

you don't understand how this proof works or induction in general?
Click to expand...


I understand this proof when it is done in induction, and i understand induction. I just dont understand why the summation in this particular problem is equal to (n+1)!-1
 
Originally posted by: chiwawa626
I understand this proof when it is done in induction, and i understand induction. I just dont understand why the summation in this particular problem is equal to (n+1)!-1
Click to expand...

??? if you understand induction and you understand the proof than why don't you understand why the summation is what it is? 😕 perhaps you don't understand induction.

edit: n/m my mistake.
edit again: now I'm confusing myself... this proof is correct, so why don't you understand it... again I go back to do you understand induction?
 
Originally posted by: fivespeed5
Originally posted by: chiwawa626
I understand this proof when it is done in induction, and i understand induction. I just dont understand why the summation in this particular problem is equal to (n+1)!-1
Click to expand...

??? if you understand induction and you understand the proof than why don't you understand why the summation is what it is? 😕 perhaps you don't understand induction.
Click to expand...

He wants to know why the CONCEPT works, he knows that it's true, he just wants to know the explanation as to why. I always wondered that too, how they figured out stuff like this. Why is it that this sum exactly equals (n+1)! - 1 ?

-silver
 
How can you not understand induction yet are able to use it? That doesn't make sense to me.

What induction does is say that "if case A is true, then Case A+1 MUST be true as well." What the base case does is supply a reference point.

Case 1 is true.
If case 1 is true, then case 2 is true.
If case 2 is true, then case 3 is true.
If case 3 is true, then case 4 is true.
etc....

Because you carry this to infinity then every case must be true.

Induction is a perfectly valid form of proof.

Edit: I saw the posts above mine and want to add something. Induction is an easy way to prove or disprove something like this is equal in all cases. However, induction doesn't help you come up with the equation for what is ie equal to. That is much harder. If someone were to give you some weird equation (like sum of i*i! from i=1 to n) and wanted you to come up with what it equaled, induction would be of little help. If they gave you the equation and an answer then induction would let you easily prove/disprove that it is correct.
 
ahhh! (screaming)

I UNDERSTAND INDUCTION. I UNDERSTAND THE PARTICULAR PROOF I LINKED.

But i do not understand the concept of why the series 1*1! + 2*2! + 3*3! ... n*n! = (n+1)! - 1

If you were to do a proof that WAS NOT BY INDUCTION then you would show a method to making the left side equal the right side, am i correct? I dont see how one can derive this general formula for the sum. That is what i want to see, a proof for this problem that is NOT BY INDUCTION, so you can see how it actualy works. Induction proves its true, but dosent explain why or how to arrive at this conclusion.
 
Originally posted by: chiwawa626
ahhh! (screaming)

I UNDERSTAND INDUCTION. I UNDERSTAND THE PARTICULAR PROOF I LINKED.

But i do not understand the concept of why the series 1*1! + 2*2! + 3*3! ... n*n! = (n+1)! - 1

If you were to do a proof that WAS NOT BY INDUCTION then you would show a method to making the left side equal the right side, am i correct? I dont see how one can derive this general formula for the sum. That is what i want to see, a proof for this problem that is NOT BY INDUCTION, so you can see how it actualy works. Induction proves its true, but dosent explain why or how to arrive at this conclusion.
Click to expand...

Induction DOES explain why they arrived at the conclusion. Look at the first 2 steps of induction and you will see why. There's probably a way to explain why the series is equal to what it is but not a proof in the classical sense (ie massaging the left to equal the right).

You seriously do not understand induction if you understand how the proof you linked explains the series.
 
Induction DOES explain why they arrived at the conclusion. Look at the first 2 steps of induction and you will see why. There's probably a way to explain why the series is equal to what it is but not a proof in the classical sense (ie massaging the left to equal the right).
Click to expand...

Mabey you still dont see what im saying. Yes induction obviously proves s(n) is equal to (n+1)!-1...but it dosent provide a method for showing how one would derive (n+1)!-1. You can always prove stuff by induction, but a lot of the time it dosent give you a full reason to why it works. How did the guy who made this theorum or whatever exactly figure out that s(n) is equal to (n+1)!-1, thats what i want to know, and thats not what induction tells me.
 
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