Sum of series sin(n*x)

sin(x) + sin(2*x) + sin(3*x) + sin(4*x) + sin(5*x) + sin(6*x) + sin(7*x) + sin(8*x) + sin(9*x) + sin(10*x) + sin(11*x) + sin(12*x) + sin(13*x) + sin(14*x) + sin(15*x) + sin(16*x) + sin(17*x) + sin(18*x) + sin(19*x) + sin(20*x) + sin(21*x) + sin(22*x) + sin(23*x) + sin(24*x) + sin(25*x) + sin(26*x) + sin(27*x) + sin(28*x) + sin(29*x) + sin(30*x) + sin(31*x) + sin(32*x) + sin(33*x) + sin(34*x) + sin(35*x) + sin(36*x) + sin(37*x) + sin(38*x) + sin(39*x) + sin(40*x) + sin(41*x) + sin(42*x) + sin(43*x) + sin(44*x) + sin(45*x) + sin(46*x) + sin(47*x) + sin(48*x) + sin(49*x) + sin(50*x) + sin(51*x) + sin(52*x) + sin(53*x) + sin(54*x) + sin(55*x) + sin(56*x) + sin(57*x) + sin(58*x) + sin(59*x) + sin(60*x) + sin(61*x) + sin(62*x) + sin(63*x) + sin(64*x) + sin(65*x) + sin(66*x) + sin(67*x) + sin(68*x) + sin(69*x) + sin(70*x) + sin(71*x) + sin(72*x) + sin(73*x) + sin(74*x) + sin(75*x) + sin(76*x) + sin(77*x) + sin(78*x) + sin(79*x) + sin(80*x) + sin(81*x) + sin(82*x) + sin(83*x) + sin(84*x) + sin(85*x) + sin(86*x) + sin(87*x) + sin(88*x) + sin(89*x) + sin(90*x) + sin(91*x) + sin(92*x) + sin(93*x) + sin(94*x) + sin(95*x) + sin(96*x) + sin(97*x) + sin(98*x) + sin(99*x) + sin(100*x)

$$\sin{\left(x \right)} + \sin{\left(2 x \right)} + \sin{\left(3 x \right)} + \sin{\left(4 x \right)} + \sin{\left(5 x \right)} + \sin{\left(6 x \right)} + \sin{\left(7 x \right)} + \sin{\left(8 x \right)} + \sin{\left(9 x \right)} + \sin{\left(10 x \right)} + \sin{\left(11 x \right)} + \sin{\left(12 x \right)} + \sin{\left(13 x \right)} + \sin{\left(14 x \right)} + \sin{\left(15 x \right)} + \sin{\left(16 x \right)} + \sin{\left(17 x \right)} + \sin{\left(18 x \right)} + \sin{\left(19 x \right)} + \sin{\left(20 x \right)} + \sin{\left(21 x \right)} + \sin{\left(22 x \right)} + \sin{\left(23 x \right)} + \sin{\left(24 x \right)} + \sin{\left(25 x \right)} + \sin{\left(26 x \right)} + \sin{\left(27 x \right)} + \sin{\left(28 x \right)} + \sin{\left(29 x \right)} + \sin{\left(30 x \right)} + \sin{\left(31 x \right)} + \sin{\left(32 x \right)} + \sin{\left(33 x \right)} + \sin{\left(34 x \right)} + \sin{\left(35 x \right)} + \sin{\left(36 x \right)} + \sin{\left(37 x \right)} + \sin{\left(38 x \right)} + \sin{\left(39 x \right)} + \sin{\left(40 x \right)} + \sin{\left(41 x \right)} + \sin{\left(42 x \right)} + \sin{\left(43 x \right)} + \sin{\left(44 x \right)} + \sin{\left(45 x \right)} + \sin{\left(46 x \right)} + \sin{\left(47 x \right)} + \sin{\left(48 x \right)} + \sin{\left(49 x \right)} + \sin{\left(50 x \right)} + \sin{\left(51 x \right)} + \sin{\left(52 x \right)} + \sin{\left(53 x \right)} + \sin{\left(54 x \right)} + \sin{\left(55 x \right)} + \sin{\left(56 x \right)} + \sin{\left(57 x \right)} + \sin{\left(58 x \right)} + \sin{\left(59 x \right)} + \sin{\left(60 x \right)} + \sin{\left(61 x \right)} + \sin{\left(62 x \right)} + \sin{\left(63 x \right)} + \sin{\left(64 x \right)} + \sin{\left(65 x \right)} + \sin{\left(66 x \right)} + \sin{\left(67 x \right)} + \sin{\left(68 x \right)} + \sin{\left(69 x \right)} + \sin{\left(70 x \right)} + \sin{\left(71 x \right)} + \sin{\left(72 x \right)} + \sin{\left(73 x \right)} + \sin{\left(74 x \right)} + \sin{\left(75 x \right)} + \sin{\left(76 x \right)} + \sin{\left(77 x \right)} + \sin{\left(78 x \right)} + \sin{\left(79 x \right)} + \sin{\left(80 x \right)} + \sin{\left(81 x \right)} + \sin{\left(82 x \right)} + \sin{\left(83 x \right)} + \sin{\left(84 x \right)} + \sin{\left(85 x \right)} + \sin{\left(86 x \right)} + \sin{\left(87 x \right)} + \sin{\left(88 x \right)} + \sin{\left(89 x \right)} + \sin{\left(90 x \right)} + \sin{\left(91 x \right)} + \sin{\left(92 x \right)} + \sin{\left(93 x \right)} + \sin{\left(94 x \right)} + \sin{\left(95 x \right)} + \sin{\left(96 x \right)} + \sin{\left(97 x \right)} + \sin{\left(98 x \right)} + \sin{\left(99 x \right)} + \sin{\left(100 x \right)}$$

sin(x) + sin(2*x) + sin(3*x) + sin(4*x) + sin(5*x) + sin(6*x) + sin(7*x) + sin(8*x) + sin(9*x) + sin(10*x) + sin(11*x) + sin(12*x) + sin(13*x) + sin(14*x) + sin(15*x) + sin(16*x) + sin(17*x) + sin(18*x) + sin(19*x) + sin(20*x) + sin(21*x) + sin(22*x) + sin(23*x) + sin(24*x) + sin(25*x) + sin(26*x) + sin(27*x) + sin(28*x) + sin(29*x) + sin(30*x) + sin(31*x) + sin(32*x) + sin(33*x) + sin(34*x) + sin(35*x) + sin(36*x) + sin(37*x) + sin(38*x) + sin(39*x) + sin(40*x) + sin(41*x) + sin(42*x) + sin(43*x) + sin(44*x) + sin(45*x) + sin(46*x) + sin(47*x) + sin(48*x) + sin(49*x) + sin(50*x) + sin(51*x) + sin(52*x) + sin(53*x) + sin(54*x) + sin(55*x) + sin(56*x) + sin(57*x) + sin(58*x) + sin(59*x) + sin(60*x) + sin(61*x) + sin(62*x) + sin(63*x) + sin(64*x) + sin(65*x) + sin(66*x) + sin(67*x) + sin(68*x) + sin(69*x) + sin(70*x) + sin(71*x) + sin(72*x) + sin(73*x) + sin(74*x) + sin(75*x) + sin(76*x) + sin(77*x) + sin(78*x) + sin(79*x) + sin(80*x) + sin(81*x) + sin(82*x) + sin(83*x) + sin(84*x) + sin(85*x) + sin(86*x) + sin(87*x) + sin(88*x) + sin(89*x) + sin(90*x) + sin(91*x) + sin(92*x) + sin(93*x) + sin(94*x) + sin(95*x) + sin(96*x) + sin(97*x) + sin(98*x) + sin(99*x) + sin(100*x)