What Are the Discontinuities of the Function g on the Interval [0,1]?

[foxjwill]

Homework Statement

Find (and prove as such) all discontinuities of the function g:[0,1]\to\mathbb{R} given by

g(x)=\sum_{n=1}^\infty \frac{1}{2^{2n-1}}\left\lfloor \frac{2^nx+1}{2} \right\rfloor​

where \lfloor\cdot\rfloor is the greatest integer function.

Homework Equations

The Attempt at a Solution

I'm pretty sure that the discontinuities all occur at x=(2k+1)2^{-m} for positive integer k,m since this is where the expression inside the greatest integer function is an integer. The thing is, I have no how to go about proving that these points are discontinuous. Can anyone steer me in the right direction?

 

[Office_Shredder]

When x hits that point, note that every term in the sum is
1) positive
2) larger when you cross over the point

And you get that as you approach (2k+1)2^-m from the right, each term is strictly larger than when you approach from the left