The question has been addressed, but for completeness I should like to remark that the most thorough and readily understandable discussion of Olber's Paradox is that of E. Harrison in his book Cosmology, the Science of the Universe (CUP 2000).
It is also worth remarking that we now know that the sky at night is not in fact dark: the light from the cosmic microwave background (CMB) dominates all other sources of radiation, including the sum total of all the stars. Most of the CMB radiation comes out in the microwave region of the electromagnetic spectrum. This was discussed by M. Longair and R.A. Sunyaev in the journal Astrophysical Letters (vol 4 pp65-70 1969) with the following sketch
Updates on this were published in 1990 by M. Ressell and M. Turner (Comments on Astrophysics, vol 14 p323) and by R. Henry in 1999 (Astrophys. J. Vol 516 pp. L49-L52).
So the sky is not dark at night. The light of the night sky is due to the CMB and not due to stars. The finite lifetime of stars, the finite age of the universe and the cosmic expansion have together reduced the contribution from starlight.