# Maximizing a nested sum of infinitely many variables (discrete variational calculus)

I am wondering if there is a way of finding a neat closed form solution for a series of numbers $$r_t$$ that satisfies the following. This is supposed to give the optimal strategy of an economic agent with exponential discounting of utilities.

$$\max_{r_t=0...\infty } (\sum_{t=0}^{\infty}(\delta^t\sqrt{b^2r_t^2-\beta(\varepsilon _0-\alpha b \sum_{k=0}^{t}r_k)^2} ))$$

What kind of techniques would one use to approach such a problem?

Sorry if the LaTeX is a mess. I am new to this site and don't have a lot of advanced math background.