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The branching fraction for the decay $D^+_s\to\tau^{+}\nu_{\tau}$, with$\tau^{+}\to e^{+} \nu_{e}\bar{\nu}_{\tau}$, is measured using a data samplecorresponding to an integrated luminosity of 427 fb^{-1} collected at center ofmass energies near 10.58 GeV with the \slshape B\kern-0.1em{\smallerA}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R} detector at the PEP-IIasymmetric-energy $e^{+}e^{-}$ collider at SLAC. In the process $e^{+}e^{-}\toc\bar c\to D^{*+}_s \kern 0.2em\bar{\kern -0.2em D}{}_{\mathrm{TAG}} \kern0.2em\bar{\kern -0.2em K}{} X$, the $D^{*+}_s$ meson is reconstructed as amissing particle, and the subsequent decay $D^{*+}_s\to D^+_s\gamma$ yields aninclusive $D^+_s$ data sample. Here $_{\mathrm{TAG}}$ refers to a fullyreconstructed hadronic $\kern 0.2em\bar{\kern -0.2em D}{}$ decay, $\kern0.2em\bar{\kern -0.2em K}{}$ is a $K^-$ or $\kern 0.2em\bar{\kern -0.2emK}{}^0$, and $X$ stands for any number of charged or neutral pions. The decay$D^+_s\to K^0_{\scriptscriptstyle S} K^{+}$ is isolated also, and from ratio ofevent yields and known branching fractions, ${\cal B}(D^+_s\to\tau^{+}\nu_{\tau})$ = (4.5\pm0.5\pm0.4\pm0.3% is determined. Thepseudoscalar decay constant is extracted to be $f_{D_s}$ = (233\pm13\pm10\pm7)MeV, where the first uncertainty is statistical, the second is systematic, andthe third results from the uncertainties on the external measurements used asinput to the calculation.

Measurement of the Branching Fraction for $D^+_s\to\tau^{+}\nu_{\tau}$ and Extraction of the Decay Constant f_{D_s}