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May 1st, 2010, 09:19 AM  #1 
Newbie Joined: May 2010 Posts: 1 Thanks: 0  Inducition problem with Factorial terms
Hello, I'm studying Discrete mathematics and am stuck at a particular point in an assisgnment where i have to use mathematical induction to prove that every n > 0 is true the assignment is: 1 . 1! + 2 . 2! + ... + n . n! = (n+1)!  1 so we enter P(o) which comes out 0. This implies that P(o) > P(n+1) so we have an induction hypothesis and we want to prove: 1 . 1! + 2 . 2! + ... + n . n! + (n+1) . (n+1)! = (n+1+1)!  1 simplify and replace the summation with the original data: (n+1)!  1 + (n+1) . (n+1)! = (n+2)!  1 so this is where I'm stuck because I don't know how to simplify the LHS to be equal to the right handside because the math includes factorial terms which I have never used before. (The anwser is not at the back of the book) Thanks in advance, Rijsthoofd 
May 1st, 2010, 01:03 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,759 Thanks: 696  Re: Inducition problem with Factorial terms
(n+1)!  1 + (n+1) . (n+1)! = 1.(n+1)! + (n+1) . (n+1)! 1 = (n+2).(n+1)!  1 = (n+2)!  1


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factorial, inducition, problem, terms 
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