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May 1st, 2010, 09:19 AM   #1
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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
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May 1st, 2010, 01:03 PM   #2
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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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