N=2, using , prove

Let , and

The following is my algebraic work:

=

=

=

=

=

How do you go from here to

I posted the above yesterday morning, earnesty not knowing the solution, and I spent all night contemplating and discovered that the solution to the proof is only true in a special case of Binomial distribution, since the Standard Deviation in Binomial Distribution is , where of the given in the question.

In this case . Therefore, is required for all cases regardless, and for the solution, there is no other sample space but that of S={a, a+1},

Now, case closed.