# Confusion with integration of sums

Hello guys, since I am new at sums and multivariable calculus I faced a problem when I stumbled upon this: $$\sum_{r=0}^{k} \binom{n}{4r+1} x^{n-4r-1} y^{4r+1} = \sum_{r=0}^{b} \binom{n}{4r+3} x^{n-4r-3} y^{4r+3}$$ Well, the problem is that I don't know if it's possible to put a limit in every part of the equation and then convert it to an integral (I am trying to prove that $$\forall x , y \in \mathbb{R}, \quad \exists n \in \mathbb{N} , n \in \mathbb{N} , n \neq 0$$ so that the relation holds). Can I do it or does it violate any rule? And if it is possible to do it how would the multivariable integration be? (If you want the relations between n, k, b just ask)