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The decay $B_c^+\to J/\psi K^+$ is observed for the first time using a data sample, corresponding to an integrated luminosity of 1.0 ${\,fb}^{-1}$, collected by the LHCb experiment in $pp$ collisions at a centre-of-mass energy of $7\mathrm{\,Te\kern -0.1em V}$.
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