Determine whether or not the following series converges. 
Definitions:
Pentadienyl Cation
A positively charged ion with a structure derived from pentadiene, typically involved in organic reactions.
LUMO
The Lowest Unoccupied Molecular Orbital, representing the lowest-energy orbital that can accept an electron.
Allyl Anion
A negatively charged ion (an anion) consisting of a propene molecule missing one of its hydrogen atoms, known for its reactivity in organic synthesis.
Carbon p Orbitals
The set of three mutually perpendicular orbitals (px, py, pz) in a carbon atom that are involved in bonding through the overlap with orbitals from other atoms.
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