Recent content by lasindi

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...