2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76824In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Latała on bounds on moments of such sums. We also give a new proof of Latała's result for nonnegative random variables, and improve one of the constants in his inequality.Also available at http://www.math.missouri.edu/~stephen/preprints/ProbabilityFunctional Analysis60G50text