  We recently used near-infrared spectroscopy to improve the characterization
of 76 low-mass stars around which K2 had detected 79 candidate transiting
planets. Thirty of these worlds were new discoveries that have not previously
been published. We calculate the false positive probabilities that the
transit-like signals are actually caused by non-planetary astrophysical
phenomena and reject five new transit-like events and three previously reported
events as false positives. We also statistically validate 18 planets (eight of
which were previously unpublished), confirm the earlier validation of 21
planets, and announce 17 newly discovered planet candidates. Revising the
properties of the associated planet candidates based on the updated host star
characteristics and refitting the transit photometry, we find that our sample
contains 20 planets or planet candidates with radii smaller than 1.25 Earth
radii, 20 super-Earths (1.25-2 Earth radii), 20 small Neptunes (2-4 Earth
radii), three large Neptunes (4-6 Earth radii), and eight giant planets (> 6
Earth radii). Most of these planets are highly irradiated, but EPIC
206209135.04 (K2-72e, Rp = 1.29 (-0.13/+0.14) Earth radii), EPIC 211988320.01
(Rp = 2.86 (-0.15/+0.16) Earth radii), and EPIC 212690867.01 (Rp = 2.20
(-0.18/+0.19) Earth radii) orbit within optimistic habitable zone boundaries
set by the "recent Venus" inner limit and the "early Mars" outer limit. In
total, our planet sample includes eight moderately-irradiated 1.5-3 Earth
radius planet candidates (Fp < 20 F_Earth) orbiting brighter stars (Ks < 11)
that are well-suited for atmospheric investigations with Hubble, Spitzer,
and/or the James Webb Space Telescope. Five validated planets orbit relatively
bright stars (Kp < 12.5) and are expected to yield radial velocity
semi-amplitudes of at least 2 m/s.
