Please help me to solve the following problem :
Let $\Omega$ be a locally compact Hausdorff space, and suppose that the $C^{*}$-algebra $C_{0}(\Omega)$ is generated by a sequence of projections $(p_{n})_{n=1}^\infty$.
Then the hermitian element $h=\sum_{n=1}^\infty \frac{p_{n}}{3^{n}}$ generates $C_{0}(\Omega)$