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,