Nima Rashidi: Konvergenskriterier för serier

Abstract:

This essay is about convergence tests of real series. I have presented the proof of each theorem in the most educational way possible. The goal of this work is to be able to illustrate the proofs in as easy to understand language as possible in such a way that everyone, even those with different backgrounds, can enjoy reading and following it. The essay begins with a little repetition of convergence tests but with a different proof than the one we read in Analysis A and then I focused on ”new” convergence tests. Among others, I can mention a few such as Dirichlet’s, Cauchy, Ces`aro, Raabe, Abel, etc. I have also covered various examples where I showed which convergence test works for each example.