Understanding Kronig-Penney Model in Solid-State Physics

[ehrenfest]

Homework Statement

This question refers to Kittel's solid-state physics book.

On this page, in the section about the "Kronig-Penney Model in Reciprocal Space", I do not understand why the sum over s is from 0 to 1/a. What if a is 2?

Also, how do they know that "the boundary conditions are periodic over a ring of unit length"?

Homework Equations

The Attempt at a Solution

 

[malawi_glenn]

Then you only sum over zero.