Math Is Fun Forum

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

You are not logged in.

#1 2008-10-22 04:19:44

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

#2 2008-10-22 04:21:56

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)

Offline

#3 2008-10-22 05:33:48

Dulce
Guest

Re: Factorial Algebra

Daniel123 wrote:

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?

#4 2008-10-22 05:46:13

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Factorial Algebra

Dulce wrote:

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)

Offline

#5 2008-10-22 05:53:28

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.)

#6 2008-10-22 20:15:39

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!

Board footer

Powered by FluxBB