# Prove

• Nov 7th 2012, 10:29 AM
franios
Prove
A real sequence {gn} has a conxtant ratio r, that is, gn+1/gn=r for all n >0 if and only if gn=g0rn for all n>0.
• Nov 7th 2012, 10:43 AM
Plato
Re: Prove
Quote:

Originally Posted by franios
A real sequence {gn} has a constant ratio r, that is, gn+1/gn=r for all n >0 if and only if gn=g0rn for all n>0.

Use induction.
• Nov 7th 2012, 12:59 PM
franios
Re: Prove
How would I use induction?
• Nov 7th 2012, 01:06 PM
Plato
Re: Prove
Quote:

Originally Posted by franios
How would I use induction?

Is it true for the base case, $n=0~?$

If it is true that $g_K=g_0r^K$ is it true for $g_{K+1}$.

That is one part. What is the other direction?