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**1. Homework Statement**

Show that the Hubble profile of surface brightness

[tex]I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}[/tex]

leads to an infinite total luminosity. r is the distance from the center and R is a constant.

**2. The attempt at a solution**

For large r this is related as

[tex]I(r) \propto r^{-2}[/tex]

but how is the surface brightness related to the total luminosity?