A real sequence {g_{n}} has a conxtant ratio r, that is, g_{n+1}/g_{n}=r for all n >0 if and only if g_{n}=g_{0}r^{n} for all n>0.
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Originally Posted by franios A real sequence {g_{n}} has a constant ratio r, that is, g_{n+1}/g_{n}=r for all n >0 if and only if g_{n}=g_{0}r^{n} for all n>0. Use induction.
How would I use induction?
Originally Posted by franios How would I use induction? Is it true for the base case, $\displaystyle n=0~?$ If it is true that $\displaystyle g_K=g_0r^K$ is it true for $\displaystyle g_{K+1}$. That is one part. What is the other direction?
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