It is easy to prove that for $0<q<1$, $\sum_{k=0}^{n} q^{(2k+1)^{3/2}}$ converges because it is always increasing and it is always smaller than the convergent series $\sum_{k=0}^{n} q^{2k+1}$ since $0<q<1$. But then how could we find the limit of the first sum?
2026-03-25 20:20:28.1774470028
limit of $\sum_{k=0}^{n} q^{(2k+1)^{3/2}}$ with $0<q<1$?
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