Originally Posted by

**Rijsthoofd** 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)

The base case is 1.1!=(1+1)!-1, as the first n (or k) is 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

(n+1)!(1)+(n+1)!(n+1)=(n+1)!(n+1+1)=(n+1)!(n+2)

=(n+2)(n+1)(n)(n-1)....=(n+2)!

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