  The decays $B^+_c \rightarrow J/\psi D_s^+$ and $B^+_c \rightarrow J/\psi
D_s^{*+}$ are observed for the first time using a dataset, corresponding to an
integrated luminosity of 3$fb^{-1}$, collected by the LHCb experiment in
proton-proton collisions at centre-of-mass energies of $\sqrt{s}$=7 and 8 TeV.
The statistical significance for both signals is in excess of 9 standard
deviations. The following ratios of branching fractions are measured to be
$BR(B^+_c \rightarrow J/\psi D_s^+)/BR(B^+_c \rightarrow J/\psi \pi+) = 2.90
\pm 0.57 \pm 0.24$, $BR(B^+_c \rightarrow J/\psi D_s^{*+}) / BR (B^+_c
\rightarrow J/\psi D_s^+) = 2.37 \pm 0.56 \pm 0.10$, where the first
uncertainties are statistical and the second systematic. The mass of the \Bc
meson is measured to be $m_{B^+_c} = 6276.28 \pm 1.44 (stat) \pm 0.36(syst)
MeV/c^2$, using the $B^+_c \rightarrow J/\psi D_s^+$ decay mode.
