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We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large-D perturbative expansion beyond the leading order, including corrections up to 1/D^4. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics anddoi:10.1007/jhep05(2018)104 fatcat:gsht2zw7qzbsdlerq35i63o434