Thanks for the reply! It turned out that the plain old geometric upper bound was sufficient for what I was doing before, but now I need a lower bound for the following sum for x \in (0,1).
\sum_{k=0}^n [x^k + x^{k(k+1)/2} - 1]
Clearly as n goes to infinity, this sum goes to negative...
Closed form for "geometricish" series (index squared in the exponent)?
Hi all,
Is there a nice closed form for the following series?
\sum_{k=0}^n x^{k^2}
Even a decently tight upper bound and lower bound would be nice (obviously it is bounded by the corresponding geometric series \sum...