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math.HO2018★ 1 cited
A Short and Unified Proof of Kummer's Test
Tord Sjödin
Kummer's test from 1835 states that the positive series is convergent if and only if there is a sequence of positive numbers such that $…
math.HO2017
Archimedian Theorems for Composite Solids
Tord Sjödin
We consider the Center of Gravity of a solid, partly filled with some homogeneous material, and find its qualitative and quantitative properties. In particular, we prove that the C…
math.HO2013
A short proof of d'Alemberts theorem
Tord Sjödin
A classical theorem of d'Alembert states that if a polynomial P(x) with real coefficients has a non-real root x=a+ib, then it also has a root x=a-ib. We give a short and elementary…