Math Is Fun Forum

Dulce

Guest

Factorial Algebra

This questions seems so simple, but I'm kind of stumped by the fact that it has factorials. I'm not sure how to go around solving it. >_<

Basically, it says,

Show that

There's also a bit before this question which tells me to

Prove that if f(r)=r!, then f(r+1)-f(r)=r x r!.

However, I'm not sure about this either. >_<

Please help me. Thank you in advance

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Factorial Algebra

Multiply through by r! for the first question and and see what happens.

For the second: f(r+1) - f(r) = (r+1)! - r! = (r+1)r! - r! = r![(r+1) - 1] = r!r

Last edited by Daniel123 (2008-10-22 04:24:56)

Dulce

Guest

Re: Factorial Algebra

Multiply through by r! for the first question and and see what happens.

For the second: f(r+1) - f(r) = (r+1)! - r! = (r+1)r! - r! = r![(r+1) - 1] = r!r

I never knew that you could take out a factor of r! from (r+1)!.

But I'm still not sure what to do for the first bit.

Where would that lead me?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Factorial Algebra

I never knew that you could take out a factor of r! from (r+1)!.

(r+1)! = (r+1).(r).(r-1).(r-2)...3.2.1 = (r+1)r!

But I'm still not sure what to do for the first bit.

Where would that lead me?

You've not multiplied correctly. Anyway, I wouldn't really set it out like that - it was just to give you an idea.

Last edited by Daniel123 (2008-10-22 05:48:23)

Dulce

Guest

Re: Factorial Algebra

Oh dear. I'm still not getting this, I haven't done fractions with factorials in them. >_< Er... I might see my teacher because I think we've missed some important stuff out (as we're doing FP1 without having first completed C1 and C2 beforehand.)

Macy

Guest

Re: Factorial Algebra

If you rearrange that fraction in the order of (r-1)!r you will see it.

(r-1)! r  = 1 x 2 x 3 x .....(r-1) x (r-1+1) = 1 x 2 x 3 x .....(r-1) x r = r!