Proof by induction help please

[sgacedas13]

Prove that 1*1! + 2*2! + 3*3!+...+ n*n!= (n+1)!-1 whenever n is a positive integer.

Ive been stuck for a bit on it. Thanks

 

[JeffM]

Prove that 1*1! + 2*2! + 3*3!+...+ n*n!= (n+1)!-1 whenever n is a positive integer.

Ive been stuck for a bit on it. Thanks

Do you understand how to do a proof by mathematical induction?

What is the first step? Can you do it?

How do you start the second step?

 

[thepillow]

Prove that 1*1! + 2*2! + 3*3!+...+ n*n!= (n+1)!-1 whenever n is a positive integer.

Ive been stuck for a bit on it. Thanks

There's a nice little introduction to proofs by induction from the University of Sydney that you can find here: http://sydney.edu.au/stuserv/documents/maths_learning_centre/induction.pdf


Here are a few little hints to get you started:

Since you're dealing with all the positive integers, you want to start off by thinking about what happens when n = 1. Is your proposition true?

Then, the basic strategy is to show that if it's true for n = 1 then it must be true for n = 2, and if it's true for n = 2 then it must be true for n = 3, etc. This can be accomplished by showing that if it's true for n = some positive integer k, then it must also be true for the next largest positive integer n = k+1).

By doing this you will have proved that it must be true for every positive integer.

I hope that helps you get started. See what you can come up with!