My Math Forum Inducition problem with Factorial terms

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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: 6,820 Thanks: 722 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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