Homework Help: Factorial simplifying

1. Dec 7, 2008

kathrynag

1. The problem statement, all variables and given/known data

I'm trying to prove k*(k!)=(k+1)!-1

2. Relevant equations

3. The attempt at a solution
This is how far I've gotten:
k[k(k-1)(k-2)....1)]

2. Dec 7, 2008

mutton

What you are trying to prove is not true for all k.

3. Dec 7, 2008

kathrynag

Ok, but then what would I do since I know it's true for k=1

4. Dec 7, 2008

mutton

Are you sure the question doesn't say k * k! = (k + 1)! - k!?

5. Dec 7, 2008

kathrynag

No, I'm positive. Just checked in the book.

6. Dec 7, 2008

mutton

Plug in k = 2 to see that it's false.

7. Dec 7, 2008

kathrynag

Ok, so if I was given this question. I just write only true for k=1?

8. Dec 7, 2008

kathrynag

Well it's 1*1!+2*2!+...+k*k!=(k + 1)! - k!

9. Dec 7, 2008

mutton

That's not true.

$$k * k! = (k + 1 - 1) k! = (k + 1) k! - 1 * k! = (k + 1)! - k!$$

10. Dec 7, 2008

kathrynag

1*1!+2*2!+...+k*k!=(k + 1)! - 1
sorry...

11. Dec 7, 2008

mutton

Okay, so how do you plan to prove this?

12. Dec 7, 2008

kathrynag

Never mind. Just figured it out!