"Algebrization" (cont)
Looking for the "Horizontal Pattern"...

Stage Corresponding term: Or...

1
1 = 1 + 0 = 1 + ( 1 - 1) 1 = 1 + 0 = ..

2
3 = 1 + 2 = 1 + ( 3 - 1) 3 = 2 + 1 = ..

3
5 = 1 + 4 = 1 + ( 5 - 1) 5 = 3 + 2 = 3 + ( 3 - 1 )

4
7 = 1 + 6 = 1 + ( 7 - 1) 7 = 4 + 3 = 4 + ( 4 - 1 )


(output) = f(⋆) = 1 + (⋆ - 1 ) ... = + ( - 1 )

N
(output) = f(N) = 1 + (N - 1 ) ... = N + ( N - 1 )
 
Thus f(N) = N + (N-1) = 2N-1

"You make it look so easy!"