No. It is the equivalent of a PC maker going “yeah. I don’t think we are going to put in a CD drive anymore because the DVD drive we have been including for years can do CDs as well”

There are still a lot of rather arbitrary decisions to make.

Is 4/pi inside or outside of the summation?

Is it (-1)^n+1 or (-1)^n with an additional negative sign in any of the other natural locations for it.

Is the e term outside of the fraction with a negative exponent, or part of the denominator.

Do you start with n=0 or n=1 (and adjust the terms inside the summation accordingly)

Did they expand (2n+1)^2?