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 August 16th, 2014, 07:33 AM #1 Newbie   Joined: Jun 2014 From: earth Posts: 11 Thanks: 0 Need Help w/ Factorial Simplification Hello, I am trying to simplify questions such as: (n + 1)!/n! (n + 2)!/n! ((n + 1)! + n! - (n - 1)!)/(n - 1)! Naturally I don't want answers for them all, however, I do know that the first one equals n + 1, and the second one equals (n + 2)(n + 1), but I don't see how to get to that answer. If anyone can do out the simplification process simply for me, that would be greatly appreciated, thanks! August 16th, 2014, 12:58 PM   #2
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Quote:
 Originally Posted by teetar Hello, I am trying to simplify questions such as: (n + 1)!/n! (n + 2)!/n! ((n + 1)! + n! - (n - 1)!)/(n - 1)! Naturally I don't want answers for them all, however, I do know that the first one equals n + 1, and the second one equals (n + 2)(n + 1), but I don't see how to get to that answer. If anyone can do out the simplification process simply for me, that would be greatly appreciated, thanks!
n! = 1.2.3......n
(n+1)! = 1.2.3......n.(n+1) = n!.(n+1) August 16th, 2014, 04:28 PM   #3
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Hello, teetar!

Do you understand basic factorials?

$\quad \dfrac{5!}{4!} \;=\;\dfrac{5\cdot\cancel{4\cdot3\cdot2\cdot1}}{ \cancel{4 \cdot3\cdot2\cdot1}} \;=\;5$

That is: $\:\dfrac{5!}{4!} \;=\;\dfrac{5\cdot\cancel{4!}}{\cancel{4!}} \;=\;5$

Quote:
 Simplify: $\:\dfrac{(n+1)!}{n!}$

$\dfrac{(n+1)!}{n!} \;=\;\dfrac{(n+1)\,\cancel{n!}}{\cancel{n!}} \;=\;n+1$

Quote:
 $\dfrac{(n + 2)!}{n!}$

$\dfrac{(n+2)!}{n!} \;=\;\dfrac{(n+2)(n+1)\,\cancel{n!}}{\cancel{n!}} \;=\;(n+2)(n+1)$

Quote:
 $\dfrac{(n + 1)! + n! - (n - 1)!}{(n - 1)!}$

$\dfrac{(n+1)! + n! - (n-1)!}{(n-1)!} \;\;=\;\;\dfrac{(n+1)!}{(n-1)!} + \dfrac{n!}{(n-1)!} - \dfrac{(n-1)!}{(n-1)!}$

$\qquad =\;\;\dfrac{(n+1)(n)\cancel{(n-1)!}}{\cancel{(n-1)!}} + \dfrac{n\cancel{(n-1)!}}{\cancel{(n-1)!}} - \dfrac{\cancel{(n-1)!}}{\cancel{(n-1)!}}$

$\qquad =\;\; (n+1)n + n - 1 \;\;=\;\;n^2 + 2n - 1$ August 18th, 2014, 11:27 AM #4 Newbie   Joined: Jun 2014 From: earth Posts: 11 Thanks: 0 Thanks a bunch for your help! Tags factorial, simplification, w or Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Chikis Elementary Math 2 September 11th, 2013 10:11 AM fran1942 Algebra 3 June 3rd, 2012 06:57 PM fran1942 Algebra 1 May 31st, 2012 12:47 AM wulfgarpro Algebra 7 April 18th, 2010 03:16 AM wulfgarpro Algebra 5 April 14th, 2010 01:13 AM

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