Finding the value of trignometric series Σ 0 ∞ cos ⁡ n x 3 n

Question

Finding the value of trignometric series       Σ          0              ∞                          cos        ⁡        n        x                    3        n

Bruno Hughes · Accepted Answer

Hint. One may write, for   x  ∈      R  ,                    cos        ⁡        n        x                    3        n              =  Re            (                                    e                          i              x                                3                    )        n    =  Re        z    n  with       z    =                            e                      i            x                          3             then one may recall that      ∑          n      =      0        ∞        z    n    =      1          1      −      z        ,        |    z      |    &amp;lt;  1.

Finding the value of trignometric series Σ 0 ∞ cos ⁡ n x 3 n

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