k = 10
u[x_] := (∑_(n = 1)^k)(Sin[((n*π*x)/6)]*((12/(((n*π))^2))*(-Sin[((n*π)/2)] + 2*Sin[((π*n)/3)] - Sin[((π*n)/6)])*
                Cos[((n*π*t)/6)]))
Table[
      Plot[u[x], {x, -1, 7}, 
        PlotStyle -> {RGBColor[1, 0.7, 0], Thickness[0.015]}, 
        PlotRange -> {{0, 6}, {-1.1, 1.1}}], {t, 0, 18, 
        0.1}]