Cn = (1/τ) 
        Integrate[
          Exp[-I n ((2 Pi)/τ) 
              t], {t, ((-β)/2), (β/2)}, 
          Assumptions -> {{β, t, τ} ∈ 
                Reals, {n} ∈ Integers, β > 0, τ > 
                0, τ > β}]

Plot[
      Refine[(β/(2  τ)) + 
          Sum[Cn*Cos[2  (Pi/τ) n t], {n, 1, 20}], {τ == 
            5, β == 1}], {t, -1, 1}, 
      PlotRange -> {-0.5, 1}]

Do[Plot[
        Refine[Cn, {τ == N, β == 1}], {n, 0, 16}, 
        PlotRange -> {-0.2, 0.5}], {N, 2, 10, 1}]