Thread: Number Theory Proof

I need to prove the following Proposition

Let N be a positive integer. Then:
1*1! + 2*2! + 3*3! + ... + n *n! = (n+1)! - 1

Originally Posted by algebrapro18

I need to prove the following Proposition

Let N be a positive integer. Then:
1*1! + 2*2! + 3*3! + ... + n *n! = (n+1)! - 1

This is a telescoping series and the sum is:



That is all but the (n+1)! from the last term and the -1 from the first cancel
with a corresponding term from the next term in the series.

RonL

Originally Posted by algebrapro18

I need to prove the following Proposition

Let N be a positive integer. Then:
1*1! + 2*2! + 3*3! + ... + n *n! = (n+1)! - 1

base case is true... n=1

assume n=k



show k+1



by hypothesis..



grouping and factoring

Thank you so much, I thought proof by induction was the way to go.

Is there also a way to do this by Combinatorial Proof because thats the section this problem was from.