Random walks on some fractals can be analysed by renormalization procedures. These techniques make it possible to obtain the Laplace transform of the first-passage time probability density function of a random walker that moves in the fractal. The calculation depends on a function that is particular to each kind of fractal. For the Sierpinski family of fractals, it has been conjectured that , where d is the dimension of the Euclidean space in which the Sierpinski fractal is embedded. We provide a proof of the conjecture that is based on the symmetries of the Sierpinski fractal.