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(FP2) How is r! a factor of (r+1)!

So in this question in series in FP2

Simplify 1/r!−1/(r+1)! 1/r! - 1/(r+1)!

And apparently this goes to (r+1)−1/(r+1)! (r+1)-1/(r+1)!

As (r+1)! (r+1)! is the common denominator

I do not understand how this is the case? Any help appreciated!
Original post by Music With Rocks
So in this question in series in FP2

Simplify 1/r!−1/(r+1)! 1/r! - 1/(r+1)!

And apparently this goes to (r+1)−1/(r+1)! (r+1)-1/(r+1)!

As (r+1)! (r+1)! is the common denominator

I do not understand how this is the case? Any help appreciated!


What can (r+1)!(r+1)! be expanded into?
Original post by Slowbro93
What can (r+1)!(r+1)! be expanded into?


r!+1! r! + 1! ?
Original post by Music With Rocks
r!+1! r! + 1! ?


Okay, let's go back on step:

How do you calculate: 5!,10!5!, 10! and n!n!
Reply 4
Avatar for Nayzar
Nayzar
16
surprised that this is a Further maths question.
(r+1)!=(r+1) x r! which makes r! a factor
take the example:
4! = 4 x 3!
so 3! is a factor of 4!
I dont do further maths btw
(edited 7 years ago)
Original post by Slowbro93
Okay, let's go back on step:

How do you calculate: 5!,10!5!, 10! and n!n!


ohhhhhhh...

so 5! 5! is 5∗4∗3∗2∗1 5*4*3*2*1 which is the same as 5∗4! 5*4!

So then (r+1)! (r+1)! is (r+1)∗r! (r+1)*r!


Is this correct?
Original post by Music With Rocks
ohhhhhhh...

so 5! 5! is 5∗4∗3∗2∗1 5*4*3*2*1 which is the same as 5∗4! 5*4!

So then (r+1)! (r+1)! is (r+1)∗r! (r+1)*r!


Is this correct?


Agreed! :biggrin:

Now can you see what you have to do? :smile:
Original post by Nayzar
surprised that this is a Further maths question.
(r+1)!=(r+1) x r! which makes r! a factor
take the example:
4! = 4 x 3!
so 3! is a factor of 4!
I dont do further maths btw


Didn't see your reply as I was busy typing mine out haha, thank you that makes sense.
Reply 8
Avatar for Alexion
Alexion
17
Original post by Nayzar
I dont do further maths btw


savage :tongue:
Original post by Slowbro93
Agreed! :biggrin:

Now can you see what you have to do? :smile:


so that means that r! r! is a multiple of (r+1)∗r! (r+1)*r! so therefore (r+1)! (r+1)! is the common denominator

I get it now, thank you very much :biggrin:
Original post by Nayzar
surprised that this is a Further maths question.
(r+1)!=(r+1) x r! which makes r! a factor
take the example:
4! = 4 x 3!
so 3! is a factor of 4!
I dont do further maths btw


Oh and it is only a part of a question not a question in itself :wink: they wouldn't want it to be nice...
Reply 11
Avatar for Nayzar
Nayzar
16
Original post by Alexion
savage :tongue:


lol nah i didnt mean it like that haha

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