Using a sample of tagged D_s decays collected near the D^*_s D_s peak production energy in e+e- collisions with the CLEO-c detector, we study the leptonic decay D^+_s to tau^+ nu_tau via the decay channel tau^+ to e^+ nu_e bar{nu}_tau. We measure B(D^+_s to tau^+ nu_tau) = (6.17 +- 0.71 +- 0.34) %, where the first error is statistical and the second systematic. Combining this result with our measurements of D^+_s to mu^+ nu_mu and D^+_s to tau^+ nu_tau (via tau^+ to pi^+ bar{nu}_tau), we determine f_{D_s} = (274 +- 10 +- 5) MeV.
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