Suma de la serie cos(x+n)

cos(1 + x) + cos(2 + x) + cos(3 + x) + cos(4 + x) + cos(5 + x) + cos(6 + x) + cos(7 + x) + cos(8 + x) + cos(9 + x) + cos(10 + x) + cos(11 + x) + cos(12 + x) + cos(13 + x) + cos(14 + x) + cos(15 + x) + cos(16 + x) + cos(17 + x) + cos(18 + x) + cos(19 + x) + cos(20 + x) + cos(21 + x) + cos(22 + x) + cos(23 + x) + cos(24 + x) + cos(25 + x) + cos(26 + x) + cos(27 + x) + cos(28 + x) + cos(29 + x) + cos(30 + x) + cos(31 + x) + cos(32 + x) + cos(33 + x) + cos(34 + x) + cos(35 + x) + cos(36 + x) + cos(37 + x) + cos(38 + x)

$$\cos{\left(x + 1 \right)} + \cos{\left(x + 2 \right)} + \cos{\left(x + 3 \right)} + \cos{\left(x + 4 \right)} + \cos{\left(x + 5 \right)} + \cos{\left(x + 6 \right)} + \cos{\left(x + 7 \right)} + \cos{\left(x + 8 \right)} + \cos{\left(x + 9 \right)} + \cos{\left(x + 10 \right)} + \cos{\left(x + 11 \right)} + \cos{\left(x + 12 \right)} + \cos{\left(x + 13 \right)} + \cos{\left(x + 14 \right)} + \cos{\left(x + 15 \right)} + \cos{\left(x + 16 \right)} + \cos{\left(x + 17 \right)} + \cos{\left(x + 18 \right)} + \cos{\left(x + 19 \right)} + \cos{\left(x + 20 \right)} + \cos{\left(x + 21 \right)} + \cos{\left(x + 22 \right)} + \cos{\left(x + 23 \right)} + \cos{\left(x + 24 \right)} + \cos{\left(x + 25 \right)} + \cos{\left(x + 26 \right)} + \cos{\left(x + 27 \right)} + \cos{\left(x + 28 \right)} + \cos{\left(x + 29 \right)} + \cos{\left(x + 30 \right)} + \cos{\left(x + 31 \right)} + \cos{\left(x + 32 \right)} + \cos{\left(x + 33 \right)} + \cos{\left(x + 34 \right)} + \cos{\left(x + 35 \right)} + \cos{\left(x + 36 \right)} + \cos{\left(x + 37 \right)} + \cos{\left(x + 38 \right)}$$

cos(1 + x) + cos(2 + x) + cos(3 + x) + cos(4 + x) + cos(5 + x) + cos(6 + x) + cos(7 + x) + cos(8 + x) + cos(9 + x) + cos(10 + x) + cos(11 + x) + cos(12 + x) + cos(13 + x) + cos(14 + x) + cos(15 + x) + cos(16 + x) + cos(17 + x) + cos(18 + x) + cos(19 + x) + cos(20 + x) + cos(21 + x) + cos(22 + x) + cos(23 + x) + cos(24 + x) + cos(25 + x) + cos(26 + x) + cos(27 + x) + cos(28 + x) + cos(29 + x) + cos(30 + x) + cos(31 + x) + cos(32 + x) + cos(33 + x) + cos(34 + x) + cos(35 + x) + cos(36 + x) + cos(37 + x) + cos(38 + x)