For

* T(n) = 1 when n = 0
* T(n) = 2T(n-1) + 1 otherwise

I know we're supposed to look for patterns and understand the problem down till we start transforming the equations with different variables. However, once I get there, I don't understand how it is done and why certain things are done.

My issue is specifically where we replace *i* with *n* at 2i ·T(n-1). However, a full explanation would be useful as well!

![picture of the unrolling method](https://i.imgur.com/1lqOMhd.jpg)