Measurement of $f_{D_s}$ Using $D_s^+\to \tau^+\nu$ and $\tau^+\to\rho^+\overline{\nu}$

Using 600 pb$^{-1}$ of $e^+e^-$ collision data at center-of-mass energy 4170 MeV with the CLEO-c detector, we measured the branching fraction of $D_s^+\to \tau^+\nu$ using the $\tau^+\to \rho^+\overline{\nu}$ decay mode. We determined the pseudoscalar decay constant $f_{D_s}$ using this and the other measurements from CLEO-c and compared the result with the predictions of unquenched lattice QCD. We also present the first measurements of the branching fractions for $D_s^+\to K^0\pi^+\pi^0$, and $D_s^+\to\pi^+\pi^0\pi^0$, and a new measurement of the branching fraction for $D_s^+\to\eta\rho^+$.