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#1
Jun 12 2013 09:12am
So my question is



N!
----
( N - 2 )!
===================================================

N X ( N - 1 ) X ( N - 2 )!
-------------------------
( N - 2 )!
===================================================

N X ( N - 1)
===================================================
N² - N

So my question is on the last calculation, I know how the N becomes N² but can't figure out how the 1 becomes N

Thanks in advance

This post was edited by ricardos on Jun 12 2013 09:17am
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#2
Jun 12 2013 09:34am
Quote (ricardos @ 12 Jun 2013 15:12)
So my question is



N!
----
( N - 2 )!
===================================================

N X ( N - 1 ) X ( N - 2 )!
-------------------------
( N - 2 )!
===================================================

N X ( N - 1)
===================================================
N² - N

So my question is on the last  calculation, I know how the N becomes N² but can't  figure out how the 1 becomes N

Thanks in advance


let me be sure that i understand the problem right: you are looking for the solution of N! / (N-2)!

N x (N - 1) = N x N - N x 1 = N^2 - N

you need to multiply each term in the parantheses with the N before them
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#3
Jun 13 2013 09:14am
at 2:02 mins he turns the (n-2)! in to a -1


(n+1)x n x (n-1) x (n-2)! - (n-2)!


= (n-2)! x ((n+1) x n x (n-1) -1)

Can some one explain me why?

(n+1)! - (n-2)! \\\\\\= (n+1) x n x (n-1) x (n-2)! - (n-2)!\ = (n-2)! x ((n+1) x n x (n-1) -1
--------------- \\\\\\\\ ------------------------------------\ --------------------------------------------------------------------
/////n! ////// ////////////\\\\\\\\\ n!//////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\n!\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

My question is how did the (n-2) became -1

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#4
Jun 13 2013 09:29am
Quote (ricardos @ 13 Jun 2013 15:14)
at 2:02 mins he turns the (n-2)! in to a -1
http://www.youtube.com/watch?v=Ck9j_FI_YRM#

(n+1)x n x (n-1) x (n-2)!  - (n-2)! extract  (n-2)! from both factors


= (n-2)! x ((n+1) x n x (n-1) -1) ....  (n-2)! x [(n+1) x n x (n-1)-1]

Can some one explain me why?

(n+1)! - (n-2)! \\\\\\= (n+1) x n x (n-1) x (n-2)! - (n-2)!\  = (n-2)! x ((n+1) x n x (n-1) -1
---------------  \\\\\\\\ ------------------------------------\    --------------------------------------------------------------------
/////n! ////// ////////////\\\\\\\\\        n!//////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\n!\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

My question is how did the (n-2) became -1


see blue

you might see it easier if you use not only () but also [] (see red)

=====================================================================

(n+1)x n x (n-1) x (n-2)! - (n-2)!

rewrite as

[(n+1)x n x (n-1)] x (n-2)! - (n-2)!

see it now?

and on the general scale

(n+1)! - (n-k)! = [(n+1) x ... x (n-k+1) ] x (n-k)! - (n-k)! = {[(n+1) x ... x (n-k+1)] - 1} x (n-k)!

This post was edited by brmv on Jun 13 2013 09:52am
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#5
Jun 13 2013 02:21pm
he factored out (n-2)! from the subtraction equation
when you factor it out the first you get (n+1)(n)(n-1)
when you factor (n-2)! out of (n-2)! you simply are left with 1
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