
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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October 22nd, 2014, 11:12 AM  #1 
Newbie Joined: Oct 2014 From: Here Posts: 17 Thanks: 0  Factorial dividing help
Hello, Can you explain to me why is the following equal? [(n!)]²/[(n+1)!]² = 1/(n+1)(n+1) Thanks 
October 22nd, 2014, 11:19 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle = \frac{n!}{(n + 1)!} \cdot \frac{n!}{(n + 1)!}$ Can you finish from here? Dan  
October 22nd, 2014, 11:59 AM  #3 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  $\displaystyle \color{blue}{[(n!)]^2/[(n+1)!]^2 =\left[\dfrac{n!}{(n+1)!}\right]^2=\left[\dfrac{n!}{n!(n+1)}\right]^2=\left[\dfrac{1}{n+1}\right]^2=\dfrac{1}{(n+1)^2}=\dfrac{1}{(n+1)(n+1)}}$
Last edited by aurel5; October 22nd, 2014 at 12:01 PM. 
October 22nd, 2014, 01:57 PM  #4 
Newbie Joined: Oct 2014 From: Here Posts: 17 Thanks: 0 
Thanks you guys it's just that I don't know what is allowed to do when there are roots with factorials My question to you, will you actually do the steps you showed me? Or you have a way to do see it and just write the final answer without the steps? 
October 22nd, 2014, 03:31 PM  #5  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
October 22nd, 2014, 05:17 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,638 Thanks: 2623 Math Focus: Mainly analysis and algebra 
Unless the steps are blindingly obvious, you should always write them down. As Dan says, it cuts down on silly mistakes. More to the point, it makes it clear for the person reading it. If what you are writing has even the vaguest chance of looking difficult or confusing, you should add a step in the middle. 
October 22nd, 2014, 05:40 PM  #7  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
such as braces, square brackets or parentheses, around the denominator: [(n!)]²/[(n+1)!]² = 1/{(n+1)(n+1)} [(n!)]²/[(n+1)!]² = 1/[(n+1)(n+1)] [(n!)]²/[(n+1)!]² = 1/((n+1)(n+1))  
October 22nd, 2014, 07:46 PM  #8  
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 390 Thanks: 70  Quote:
Please examine and see how the arithmetic is done. Quote:
 

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