Using the differential star count formula for an infinite universe of constant stellar number density and no interstellar extinction (Eq. 24.5), show that the amount of light arriving at Earth from a cone of solid angle Ω diverges exponentially as the length of the cone increases without bound (or, equivalently, as m approaches infinity). Assume that all stars in the field have the same absolute magnitude M. Hint: You may find the discussion leading up to Eq. (3.5) helpful.