I'm trying to solve the following constrained optimzation problem:

\max_{\bar{\sigma}}\left\{\left(\sum_{k=0}^{\infty }\bar{\gamma}^{k+1}\sigma_k\right)^2 \middle|\alpha-\sum_{k=0}^{\infty}\sigma^2_k=0\right\}

where

\bar{\sigma}=\{\sigma_k\}_{k=0}^{\infty},
\bar{\gamma}}\in(0,1)
\sigma_k,\alpha>0

My goal is to find an expression for the sequence supporting the optimum of the problem, but I keep getting stuck...