Is this step function expressed as a power series wrong?

Question

Here I have a step function expressed in the answer as a power series.

Please start at Note that we can write...

I think the power series is wrong as , at any x, the value is infinite. However it is supposed to be the largest integer value as in the question. If someone could expand that power series and show me what is going as I am really confused then that would be really helpful! thank the heavens for your help. I am not sure how to write in Latex so heres a screenshot of the step function expressed as a power series.

Answer 1

The 1 and 0 should be reversed in the definition of $\chi_E$.