
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 1st, 2014, 11:01 PM  #1 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3  How to prove this factorial problem?
I have a question about factorials and provide a few examples below. (ex 1) 6! = 6*5*4*3*2*1 (ex 2) 9! = 9*8*7*6*5*4*3*2*1 (ex 3) 11! = 11*10*9*8*7*6*5*4*3*2*1 (ex 4) n! = n*(n1)*(n2)*(n3)...3*2*1 So, the r th term in each factorial above is n  r + 1. For example, the 4th term in (ex 1) is 6  4 + 1= 3, the 5 th term in (ex 2) is 9  5 + 1 =5 and the 3 rd in (ex 3) is 11  3 + 1 = 9. I figured out the r th term = n  r + 1 by finding a pattern in examples 1  3 above. Can someone show me how to prove n  r + 1 for the r th term. Thanks. 
June 2nd, 2014, 12:15 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
We have 1 <= r <= n The first factor is n. The second factor is the first factor  1. The third factor is the second factor  1 is the first factor  2, and so on. The rth factor in the product is the first factor  (r  1) = n  (r  1) = n  r + 1. See? 

Tags 
factorial, problem, prove 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Law of Factorial  ducnhuandoan  Number Theory  13  June 14th, 2016 12:20 AM 
Problem with factorial manipulation  tonyfoster  Number Theory  1  March 24th, 2014 06:06 AM 
cos with factorial.  ZardoZ  Real Analysis  15  April 17th, 2013 12:47 AM 
Inducition problem with Factorial terms  rijsthoofd  Applied Math  1  May 1st, 2010 01:03 PM 
Factorial Problem  Barbarel  Number Theory  2  August 23rd, 2009 10:08 AM 