The generalized binomial formula where c does not have to be an integer says

where, with c not an integer, we interpret as , for n= 0, 1 for n= 0.

In this case, with c= 5/2, , so the term is 1, so the "x" term is (5/2)(2x)= 5/2 x as you say. as you say.

Check my arithmetic!