Partial Sum Formulas and Asymptotic Analysis

Finding a summation formula to add the first n natural numbers is easy. Finding a summation formula to add the first n reciprocals is impossible, literally. At least in terms of elementary functions. This video dives into asymptotic analysis to prove there's no "nice" formula for the harmonic numbers. It's a great application of freshman calculus, how long can you follow along? Thanks to a viewer for pointing out a mistake in the original version of this video. Thanks for watching, please like, subscribe and comment!

[@9WEAVER9]

Great video, thanks for making it!
By chance, can you let us know which books to find the Stolz-Cesàro Theorem in?
I look forward to the day when asymptotics and perturbation theory are all over CZcams math channels. Carl Bender has close to 1 million views on his first lecture video now.

[@DrMcCrady]

Thanks for your comment! Here’s a link to a big book for sequences and series from Pete L Clark at UGA. alpha.math.uga.edu/~pete/3100supp.pdf