= Solution
Extra relativistic <neutrino> species increase the <effective number of relativistic energy degrees of freedom>. At fixed <temperature> the <Hubble parameter> rises as $g_*^{1/2}$, while the standard conversion rate is unchanged. Consequently <cosmological weak freeze-out> moves to higher <temperature>, $T_F\propto g_*^{1/6}$, and the <neutron-to-proton ratio> $r_F=e^{-Q/T_F}$ increases. The initial <neutron> fraction $r_F/(1+r_F)$ therefore increases as well.
The quicker expansion also reduces the cosmic time required to cool to the <deuterium bottleneck> <temperature>: during <radiation domination>, $t\propto g_*^{-1/2}T^{-2}$ while the thermal count is roughly constant. Fewer <neutrons> decay before burning. Both factors in the <neutron> budget increase, giving \b[a larger final helium-4 mass fraction]. This is the <primordial helium response to extra relativistic species>, under the assumption that the additional species contribute mainly to expansion rather than independently changing the conversion rates.
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