I am working through some of the problems in the appendix of my algorithms book...

They are showing that is or for some constant c

The initial condition was shown to be true as long as c >= 1. They assume that the bound holds for n and then show that it holds for n+1

as long as or

What I don't get is I see that I can distribute the to get the previous result. But Why do we want this form?

Is it because I want to express in a way that I can make it comparable to ?