http://img30.imageshack.us/img30/2584/imageskr.jpg

I know roughly what has to be done here, but for some reason its not working out like the other questions, any help would be greatly appreciated!

Printable View

- Jul 5th 2009, 04:23 AMLHSProof by induction
http://img30.imageshack.us/img30/2584/imageskr.jpg

I know roughly what has to be done here, but for some reason its not working out like the other questions, any help would be greatly appreciated! - Jul 5th 2009, 04:32 AMHallsofIvy

and you want to show that .

Okay, if n= 1, .

Now suppose that, for some k, . Now . And you want to show that that is less than k+1.

Looks to me that you just need to show that ! - Jul 5th 2009, 04:43 AMLHS
Ah I see, yes, it was at that stage I got confused.

I thought to prove it you would have to rearrange the RHS to show that the summation + the next term < k+1

Why do you need to show that (k+1)/(k+2) is less than one? - Jul 6th 2009, 08:55 PMAlephZero
Here is the "rearrangement" version you wanted:

and you are done.

HallsofIvy's point was somewhat more elegant. - Jul 6th 2009, 09:17 PMmalaygoel
- Jul 6th 2009, 09:46 PMAlephZero
Whoops, forgot to type a step. Here's the "rearrangment" proof:

Thanks for pointing that out, malaygoel. - Jul 6th 2009, 10:16 PMsimplependulum

for - Jul 6th 2009, 11:13 PMLHS
I think I see why that fraction has to be less than one. That right hand side should be k+1, or whenever you add the next term to the LHS you only add one to the RHS? So that fraction we gained from the LHS has to be less than 1 for the RHS to still be greater?

Thanks guys for your help! - Jul 7th 2009, 02:42 AMProve It

.