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
Follow Math Help Forum on Facebook and Google+
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.
View Tag Cloud