http://img197.imageshack.us/img197/1866/image18tv.jpg

I would be very grateful if anyone can help :)

I think I have a way, but i'm a little dubious about it. It involves subtracting f(n) from f(n+1), and factorising out a 4

Printable View

- Sep 6th 2009, 03:25 AMLHSProof by Induction (2n+1)(7^n)-1=4x
http://img197.imageshack.us/img197/1866/image18tv.jpg

I would be very grateful if anyone can help :)

I think I have a way, but i'm a little dubious about it. It involves subtracting f(n) from f(n+1), and factorising out a 4 - Sep 6th 2009, 03:50 AMTaluivren
hint on the induction step:

can you follow from here? - Sep 6th 2009, 04:16 AMLHS
Ok, so what you have shown there is that:

So you are saying that if f(n+1) equals the original function, add a multiple of 4?

How does that prove that f(n) is a multiple of 4? - Sep 6th 2009, 04:21 AMTaluivren
do you know how proofs by induction work? Mathematical induction - Wikipedia, the free encyclopedia

1. base case: n=1 ... f(1) = 20 is divisible by 4, base case verified.

2. inductive step: suppose the statement holds for some n. show that the statement holds for n+1. And that is what i've done in the previous post. - Sep 6th 2009, 04:30 AMLHS
Sorry I'm being retarded. Yes I am meant to know how induction works :P I can do the simpler questions, this through me off as it had a n within the bracket as well as the power.

Yes, that makes perfect sense now! :D Thanks for your help, this has been bugging me!