can we find a closed form for following sum:
\begin{equation} \sum_{i=0}^{n} a^{i^2} = a^0 + a^1 + a^4+a^9 +...a^{n^2} \end{equation}
where $0<a<1$ , what if $n \rightarrow \infty$ ?
2026-03-27 20:53:59.1774644839
Definite sum of a decreasing series
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