Math Is Fun Forum

BM

Guest

Induction and Factorials.

I'm a bit stumped on a problem where I am supposed to prove that

For any positive integer n. I've started by proving the initial case, which was easy enough. Then, to attempt to prove the inductive case, I added (n+1)*(n+1)! to both sides, resulting in

The formula on the left is exactly what I'm looking for. However, I'm confused on how to get the right side of the equation looking like the form I am trying to find:

Or more simply

And basically, what I do know is that

and so forth. Using distribution, I managed to get

Anyone have any ideas? Perhaps I should be trying to do the induction from the other side?
Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Induction and Factorials.

Hi BM;

You proved it for base case already.

The inductive step, if 1) is true and then we prove it when n -> n+1 then we are done.

Part of the LHS of 2) is 1) so substitute.

Now you are allowed to do some algebra. Add 1 to both sides of 3)

Some more algebra, divide both sides by (n+1)!

Proved by induction.

---

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.

BM

Guest

Re: Induction and Factorials.

Hi!

Thanks for the reply, bobbym. That certainly solves the problem. And shows that I should've proven it by starting from the other side.

Just one question, though, what does LHS stand for?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Induction and Factorials.

Hi BM;

Shorthand for left hand side. There is also RHS.

---

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.

BM

Guest

Re: Induction and Factorials.

...Wow, now I get it completely. That is a very good way of taking care of the problem. I'll have to remember this technique. Thanks again!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Induction and Factorials.

Hi BM;

Your welcome and welcome to the forum!

---

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.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Induction and Factorials.

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