  We make extensive simulations over a spin chain model that combines the
frustrated $J_1\textrm{-}J_2$ spin chain and the long-range nonfrustrated
$(-1)^{(r-1)}r^{-\alpha}$ decay interactions through the variational matrix
product state method for both finite and infinite lengths. We study both the
ground state entanglement and phase diagram. We find that it is most entangled
in the rotation invariant long-range ordered antiferromagnetic phase, where the
entanglement scales approximately logarithmically. We determine the development
of the Majudar-Ghosh point to a disorder line from entanglement. And we
determine approximately the transition from the dimerized and incommensurate
phase of the $J_1\textrm{-}J_2$ model to a decoupled phase by studying spin
correlation and the dimerization order parameter. Some implications for
entanglement in systems with long-range interactions are stated.
