Über eine Verallgemeinerung der Bernoullischen Ungleichung. (On a generalization of Bernoulli's inequality)
The author uses MacLaurin's formula \(f(x)=(1+x)^ a- \sum^{k}_{p=0}\binom{a}{p} x^ p\) to prove \textit{L. Gerber}'s inequality [Am. Math. Mon. 75, 875-876 (1968; Zbl 0165.371)]: \[ \binom{a}{k+1}x^{k+1}[(1+x)^ a- \sum^{k}_{p=0} \binom{a}{p} x^ p]\geq 0\text{ for } k\in {\mathbb{N}}\cup \{0\},\;a\in {\mathbb{R}},\;0\neq x>-1. \] \{Since the author expands the expression in square brackets about 0, the definition \(0^ 0:=0\) should be added.\}
scientific article; zbMATH DE number 4192049