### In finding a closed-form expression for some quantity of interest like T<sub>n</sub> we go Through three stages. ¶

1. Look at small cases. This gives us insight into the problem and helps us in stages 2 and 3.

2. Find and prove a mathematical expression for the quantity of interest. (Induction so on..)

3. Find and prove a closed form for our mathematical expression.

2. Find and prove a mathematical expression for the quantity of interest. (Induction so on..)

3. Find and prove a closed form for our mathematical expression.