Two-particle pseudorapidity correlations are measured in root s(NN) = 2.76 TeV Pb + Pb, root s(NN) = 5.02 TeV p+Pb, and root s = 13 TeV pp collisions at the Large Hadron Collider (LHC), with total integrated luminosities of approximately 7 mu b(-1), 28 nb(-1), and 65 nb(-1), respectively. The correlation function CN(eta(1),eta(2))is measured as a function of event multiplicity using charged particles in the pseudorapidity range |eta| < 2.4. The correlation function contains a significant short-range component, which is estimated and subtracted. After removal of the short-range component, the shape of the correlation function is described approximately by 1 + < a(1)(2)>(1/2) eta(1) eta(2) in all collision systems over the full multiplicity range. The values of < a(1)(2)>(1/2) are consistent for the opposite-charge pairs and same-charge pairs, and for the three collision systems at similar multiplicity. The values of < a(1)(2)>(1/2) and the magnitude of the short-range component both follow a power-law dependence on the event multiplicity. The short-range component in p + Pb collisions, after symmetrizing the proton and lead directions, is found to be smaller at a given eta than in pp collisions with comparable multiplicity.