The discussion revolves around evaluating the summation \(\sum_{i=1}^{50}\frac{1}{(100-i)^{1/2}}\), which falls under the subject area of mathematical series and summation techniques. Participants are exploring methods to approach this evaluation, including numerical approximations and potential formulas.
The discussion is active, with various approaches being considered, including numerical evaluation and theoretical methods. Some participants have shared their experiences with different computational tools and methods, while others have raised concerns about the suitability of certain techniques for this specific summation.
Participants note that the problem is part of a larger numerical context, and there is mention of potential challenges due to the nature of the summand, particularly its behavior as \(i\) approaches certain values. The discussion reflects a mix of practical and theoretical considerations without reaching a consensus on a single method.
I agree. There isn't any formula I know of that will solve that, and I can't see any way of re-arranging it into a suitable form.LCKurtz said:I think you don't, at least not in terms of a nice closed formula. You can evaluate it with something like Maple or approximate it with an integral. What is the background for where this problem came from?
Euler maclaurin won't fit easily here, its for sums that can be approximated to integrals, if I'm not wrong,Count Iblis said:You can also use the Euler-Maclaurin sum formula.
vaibhav1803 said:Euler maclaurin won't fit easily here, its for sums that can be approximated to integrals, if I'm not wrong,
here the domain of the sum is really small, plus due to the square root makes it worse (see graph of 1/sqrt(x), it apparently ceases to fall/falls very slowly after a certian interval)
hence i suggest use of recursive algorithms to find it, the only way to get the accurate sum from a mathematical standpoint.