Hi Bruce,
You are right. Thank you very much for helping me with subscripts.
Rewriting my question, this is now my issue. The following, which I believe to be equal to one, does not simplify
FullSimplify[
Sum[(Subscript[a, i] + Subscript[b, i])*(Subscript[a, i] + Subscript[b, i]), i] /
(Sum[Subscript[a, i]*Subscript[a, i], i] + 2 * Sum[Subscript[a, i]*Subscript[b, i], i] + Sum[Subscript[b, i]*Subscript[b, i], i])
]
instead it just gives back the pretty printed version of the equation. Interestingly, I was able to use the Blank[] notation to get the behavior that I wanted, so I know Mathematica knows how to do this.
FullSimplify[
Sum[(a_i + b_i)*(a_i + b_i), {i, 1}]/(Sum[a_i*a_i, {i, 1}] + 2 * Sum[a_i*b_i, {i, 1}] + Sum[b_i*b_i, {i, 1}])
]
returns 1 and does some other algebra that I've tested as I expect, but it does make extremely verbose output.