Sr Examen

Suma de la serie sinn*cosn



=

Solución

Ha introducido [src]
 180               
 __                
 \ `               
  )   sin(n)*cos(n)
 /_,               
n = 0              
$$\sum_{n=0}^{180} \sin{\left(n \right)} \cos{\left(n \right)}$$
Sum(sin(n)*cos(n), (n, 0, 180))
Velocidad de la convergencia de la serie
Respuesta [src]
cos(1)*sin(1) + cos(2)*sin(2) + cos(3)*sin(3) + cos(4)*sin(4) + cos(5)*sin(5) + cos(6)*sin(6) + cos(7)*sin(7) + cos(8)*sin(8) + cos(9)*sin(9) + cos(10)*sin(10) + cos(11)*sin(11) + cos(12)*sin(12) + cos(13)*sin(13) + cos(14)*sin(14) + cos(15)*sin(15) + cos(16)*sin(16) + cos(17)*sin(17) + cos(18)*sin(18) + cos(19)*sin(19) + cos(20)*sin(20) + cos(21)*sin(21) + cos(22)*sin(22) + cos(23)*sin(23) + cos(24)*sin(24) + cos(25)*sin(25) + cos(26)*sin(26) + cos(27)*sin(27) + cos(28)*sin(28) + cos(29)*sin(29) + cos(30)*sin(30) + cos(31)*sin(31) + cos(32)*sin(32) + cos(33)*sin(33) + cos(34)*sin(34) + cos(35)*sin(35) + cos(36)*sin(36) + cos(37)*sin(37) + cos(38)*sin(38) + cos(39)*sin(39) + cos(40)*sin(40) + cos(41)*sin(41) + cos(42)*sin(42) + cos(43)*sin(43) + cos(44)*sin(44) + cos(45)*sin(45) + cos(46)*sin(46) + cos(47)*sin(47) + cos(48)*sin(48) + cos(49)*sin(49) + cos(50)*sin(50) + cos(51)*sin(51) + cos(52)*sin(52) + cos(53)*sin(53) + cos(54)*sin(54) + cos(55)*sin(55) + cos(56)*sin(56) + cos(57)*sin(57) + cos(58)*sin(58) + cos(59)*sin(59) + cos(60)*sin(60) + cos(61)*sin(61) + cos(62)*sin(62) + cos(63)*sin(63) + cos(64)*sin(64) + cos(65)*sin(65) + cos(66)*sin(66) + cos(67)*sin(67) + cos(68)*sin(68) + cos(69)*sin(69) + cos(70)*sin(70) + cos(71)*sin(71) + cos(72)*sin(72) + cos(73)*sin(73) + cos(74)*sin(74) + cos(75)*sin(75) + cos(76)*sin(76) + cos(77)*sin(77) + cos(78)*sin(78) + cos(79)*sin(79) + cos(80)*sin(80) + cos(81)*sin(81) + cos(82)*sin(82) + cos(83)*sin(83) + cos(84)*sin(84) + cos(85)*sin(85) + cos(86)*sin(86) + cos(87)*sin(87) + cos(88)*sin(88) + cos(89)*sin(89) + cos(90)*sin(90) + cos(91)*sin(91) + cos(92)*sin(92) + cos(93)*sin(93) + cos(94)*sin(94) + cos(95)*sin(95) + cos(96)*sin(96) + cos(97)*sin(97) + cos(98)*sin(98) + cos(99)*sin(99) + cos(100)*sin(100) + cos(101)*sin(101) + cos(102)*sin(102) + cos(103)*sin(103) + cos(104)*sin(104) + cos(105)*sin(105) + cos(106)*sin(106) + cos(107)*sin(107) + cos(108)*sin(108) + cos(109)*sin(109) + cos(110)*sin(110) + cos(111)*sin(111) + cos(112)*sin(112) + cos(113)*sin(113) + cos(114)*sin(114) + cos(115)*sin(115) + cos(116)*sin(116) + cos(117)*sin(117) + cos(118)*sin(118) + cos(119)*sin(119) + cos(120)*sin(120) + cos(121)*sin(121) + cos(122)*sin(122) + cos(123)*sin(123) + cos(124)*sin(124) + cos(125)*sin(125) + cos(126)*sin(126) + cos(127)*sin(127) + cos(128)*sin(128) + cos(129)*sin(129) + cos(130)*sin(130) + cos(131)*sin(131) + cos(132)*sin(132) + cos(133)*sin(133) + cos(134)*sin(134) + cos(135)*sin(135) + cos(136)*sin(136) + cos(137)*sin(137) + cos(138)*sin(138) + cos(139)*sin(139) + cos(140)*sin(140) + cos(141)*sin(141) + cos(142)*sin(142) + cos(143)*sin(143) + cos(144)*sin(144) + cos(145)*sin(145) + cos(146)*sin(146) + cos(147)*sin(147) + cos(148)*sin(148) + cos(149)*sin(149) + cos(150)*sin(150) + cos(151)*sin(151) + cos(152)*sin(152) + cos(153)*sin(153) + cos(154)*sin(154) + cos(155)*sin(155) + cos(156)*sin(156) + cos(157)*sin(157) + cos(158)*sin(158) + cos(159)*sin(159) + cos(160)*sin(160) + cos(161)*sin(161) + cos(162)*sin(162) + cos(163)*sin(163) + cos(164)*sin(164) + cos(165)*sin(165) + cos(166)*sin(166) + cos(167)*sin(167) + cos(168)*sin(168) + cos(169)*sin(169) + cos(170)*sin(170) + cos(171)*sin(171) + cos(172)*sin(172) + cos(173)*sin(173) + cos(174)*sin(174) + cos(175)*sin(175) + cos(176)*sin(176) + cos(177)*sin(177) + cos(178)*sin(178) + cos(179)*sin(179) + cos(180)*sin(180)
$$\sin{\left(172 \right)} \cos{\left(172 \right)} + \sin{\left(150 \right)} \cos{\left(150 \right)} + \sin{\left(128 \right)} \cos{\left(128 \right)} + \sin{\left(106 \right)} \cos{\left(106 \right)} + \sin{\left(84 \right)} \cos{\left(84 \right)} + \sin{\left(62 \right)} \cos{\left(62 \right)} + \sin{\left(40 \right)} \cos{\left(40 \right)} + \sin{\left(18 \right)} \cos{\left(18 \right)} + \sin{\left(15 \right)} \cos{\left(15 \right)} + \sin{\left(37 \right)} \cos{\left(37 \right)} + \sin{\left(59 \right)} \cos{\left(59 \right)} + \sin{\left(81 \right)} \cos{\left(81 \right)} + \sin{\left(103 \right)} \cos{\left(103 \right)} + \sin{\left(125 \right)} \cos{\left(125 \right)} + \sin{\left(147 \right)} \cos{\left(147 \right)} + \sin{\left(169 \right)} \cos{\left(169 \right)} + \sin{\left(175 \right)} \cos{\left(175 \right)} + \sin{\left(153 \right)} \cos{\left(153 \right)} + \sin{\left(131 \right)} \cos{\left(131 \right)} + \sin{\left(109 \right)} \cos{\left(109 \right)} + \sin{\left(87 \right)} \cos{\left(87 \right)} + \sin{\left(65 \right)} \cos{\left(65 \right)} + \sin{\left(43 \right)} \cos{\left(43 \right)} + \sin{\left(21 \right)} \cos{\left(21 \right)} + \sin{\left(12 \right)} \cos{\left(12 \right)} + \sin{\left(34 \right)} \cos{\left(34 \right)} + \sin{\left(56 \right)} \cos{\left(56 \right)} + \sin{\left(78 \right)} \cos{\left(78 \right)} + \sin{\left(100 \right)} \cos{\left(100 \right)} + \sin{\left(122 \right)} \cos{\left(122 \right)} + \sin{\left(144 \right)} \cos{\left(144 \right)} + \sin{\left(166 \right)} \cos{\left(166 \right)} + \sin{\left(178 \right)} \cos{\left(178 \right)} + \sin{\left(156 \right)} \cos{\left(156 \right)} + \sin{\left(134 \right)} \cos{\left(134 \right)} + \sin{\left(112 \right)} \cos{\left(112 \right)} + \sin{\left(90 \right)} \cos{\left(90 \right)} + \sin{\left(68 \right)} \cos{\left(68 \right)} + \sin{\left(46 \right)} \cos{\left(46 \right)} + \sin{\left(24 \right)} \cos{\left(24 \right)} + \sin{\left(2 \right)} \cos{\left(2 \right)} + \sin{\left(9 \right)} \cos{\left(9 \right)} + \sin{\left(31 \right)} \cos{\left(31 \right)} + \sin{\left(53 \right)} \cos{\left(53 \right)} + \sin{\left(75 \right)} \cos{\left(75 \right)} + \sin{\left(97 \right)} \cos{\left(97 \right)} + \sin{\left(119 \right)} \cos{\left(119 \right)} + \sin{\left(141 \right)} \cos{\left(141 \right)} + \sin{\left(163 \right)} \cos{\left(163 \right)} + \sin{\left(159 \right)} \cos{\left(159 \right)} + \sin{\left(137 \right)} \cos{\left(137 \right)} + \sin{\left(115 \right)} \cos{\left(115 \right)} + \sin{\left(93 \right)} \cos{\left(93 \right)} + \sin{\left(71 \right)} \cos{\left(71 \right)} + \sin{\left(49 \right)} \cos{\left(49 \right)} + \sin{\left(27 \right)} \cos{\left(27 \right)} + \sin{\left(5 \right)} \cos{\left(5 \right)} + \sin{\left(6 \right)} \cos{\left(6 \right)} + \sin{\left(28 \right)} \cos{\left(28 \right)} + \sin{\left(50 \right)} \cos{\left(50 \right)} + \sin{\left(72 \right)} \cos{\left(72 \right)} + \sin{\left(94 \right)} \cos{\left(94 \right)} + \sin{\left(116 \right)} \cos{\left(116 \right)} + \sin{\left(138 \right)} \cos{\left(138 \right)} + \sin{\left(160 \right)} \cos{\left(160 \right)} + \sin{\left(162 \right)} \cos{\left(162 \right)} + \sin{\left(140 \right)} \cos{\left(140 \right)} + \sin{\left(118 \right)} \cos{\left(118 \right)} + \sin{\left(96 \right)} \cos{\left(96 \right)} + \sin{\left(74 \right)} \cos{\left(74 \right)} + \sin{\left(52 \right)} \cos{\left(52 \right)} + \sin{\left(30 \right)} \cos{\left(30 \right)} + \sin{\left(8 \right)} \cos{\left(8 \right)} + \sin{\left(3 \right)} \cos{\left(3 \right)} + \sin{\left(25 \right)} \cos{\left(25 \right)} + \sin{\left(47 \right)} \cos{\left(47 \right)} + \sin{\left(69 \right)} \cos{\left(69 \right)} + \sin{\left(91 \right)} \cos{\left(91 \right)} + \sin{\left(113 \right)} \cos{\left(113 \right)} + \sin{\left(135 \right)} \cos{\left(135 \right)} + \sin{\left(157 \right)} \cos{\left(157 \right)} + \sin{\left(179 \right)} \cos{\left(179 \right)} + \sin{\left(165 \right)} \cos{\left(165 \right)} + \sin{\left(143 \right)} \cos{\left(143 \right)} + \sin{\left(121 \right)} \cos{\left(121 \right)} + \sin{\left(99 \right)} \cos{\left(99 \right)} + \sin{\left(77 \right)} \cos{\left(77 \right)} + \sin{\left(55 \right)} \cos{\left(55 \right)} + \sin{\left(33 \right)} \cos{\left(33 \right)} + \sin{\left(11 \right)} \cos{\left(11 \right)} + \sin{\left(22 \right)} \cos{\left(22 \right)} + \sin{\left(44 \right)} \cos{\left(44 \right)} + \sin{\left(66 \right)} \cos{\left(66 \right)} + \sin{\left(88 \right)} \cos{\left(88 \right)} + \sin{\left(110 \right)} \cos{\left(110 \right)} + \sin{\left(132 \right)} \cos{\left(132 \right)} + \sin{\left(154 \right)} \cos{\left(154 \right)} + \sin{\left(176 \right)} \cos{\left(176 \right)} + \sin{\left(168 \right)} \cos{\left(168 \right)} + \sin{\left(146 \right)} \cos{\left(146 \right)} + \sin{\left(124 \right)} \cos{\left(124 \right)} + \sin{\left(102 \right)} \cos{\left(102 \right)} + \sin{\left(80 \right)} \cos{\left(80 \right)} + \sin{\left(58 \right)} \cos{\left(58 \right)} + \sin{\left(36 \right)} \cos{\left(36 \right)} + \sin{\left(14 \right)} \cos{\left(14 \right)} + \sin{\left(19 \right)} \cos{\left(19 \right)} + \sin{\left(41 \right)} \cos{\left(41 \right)} + \sin{\left(63 \right)} \cos{\left(63 \right)} + \sin{\left(85 \right)} \cos{\left(85 \right)} + \sin{\left(107 \right)} \cos{\left(107 \right)} + \sin{\left(129 \right)} \cos{\left(129 \right)} + \sin{\left(151 \right)} \cos{\left(151 \right)} + \sin{\left(173 \right)} \cos{\left(173 \right)} + \sin{\left(171 \right)} \cos{\left(171 \right)} + \sin{\left(149 \right)} \cos{\left(149 \right)} + \sin{\left(127 \right)} \cos{\left(127 \right)} + \sin{\left(105 \right)} \cos{\left(105 \right)} + \sin{\left(83 \right)} \cos{\left(83 \right)} + \sin{\left(61 \right)} \cos{\left(61 \right)} + \sin{\left(39 \right)} \cos{\left(39 \right)} + \sin{\left(17 \right)} \cos{\left(17 \right)} + \sin{\left(16 \right)} \cos{\left(16 \right)} + \sin{\left(38 \right)} \cos{\left(38 \right)} + \sin{\left(60 \right)} \cos{\left(60 \right)} + \sin{\left(82 \right)} \cos{\left(82 \right)} + \sin{\left(104 \right)} \cos{\left(104 \right)} + \sin{\left(126 \right)} \cos{\left(126 \right)} + \sin{\left(148 \right)} \cos{\left(148 \right)} + \sin{\left(170 \right)} \cos{\left(170 \right)} + \sin{\left(174 \right)} \cos{\left(174 \right)} + \sin{\left(152 \right)} \cos{\left(152 \right)} + \sin{\left(130 \right)} \cos{\left(130 \right)} + \sin{\left(108 \right)} \cos{\left(108 \right)} + \sin{\left(86 \right)} \cos{\left(86 \right)} + \sin{\left(64 \right)} \cos{\left(64 \right)} + \sin{\left(42 \right)} \cos{\left(42 \right)} + \sin{\left(20 \right)} \cos{\left(20 \right)} + \sin{\left(13 \right)} \cos{\left(13 \right)} + \sin{\left(35 \right)} \cos{\left(35 \right)} + \sin{\left(57 \right)} \cos{\left(57 \right)} + \sin{\left(79 \right)} \cos{\left(79 \right)} + \sin{\left(101 \right)} \cos{\left(101 \right)} + \sin{\left(123 \right)} \cos{\left(123 \right)} + \sin{\left(145 \right)} \cos{\left(145 \right)} + \sin{\left(167 \right)} \cos{\left(167 \right)} + \sin{\left(177 \right)} \cos{\left(177 \right)} + \sin{\left(155 \right)} \cos{\left(155 \right)} + \sin{\left(133 \right)} \cos{\left(133 \right)} + \sin{\left(111 \right)} \cos{\left(111 \right)} + \sin{\left(89 \right)} \cos{\left(89 \right)} + \sin{\left(67 \right)} \cos{\left(67 \right)} + \sin{\left(45 \right)} \cos{\left(45 \right)} + \sin{\left(23 \right)} \cos{\left(23 \right)} + \sin{\left(1 \right)} \cos{\left(1 \right)} + \sin{\left(10 \right)} \cos{\left(10 \right)} + \sin{\left(32 \right)} \cos{\left(32 \right)} + \sin{\left(54 \right)} \cos{\left(54 \right)} + \sin{\left(76 \right)} \cos{\left(76 \right)} + \sin{\left(98 \right)} \cos{\left(98 \right)} + \sin{\left(120 \right)} \cos{\left(120 \right)} + \sin{\left(142 \right)} \cos{\left(142 \right)} + \sin{\left(164 \right)} \cos{\left(164 \right)} + \sin{\left(180 \right)} \cos{\left(180 \right)} + \sin{\left(158 \right)} \cos{\left(158 \right)} + \sin{\left(136 \right)} \cos{\left(136 \right)} + \sin{\left(114 \right)} \cos{\left(114 \right)} + \sin{\left(92 \right)} \cos{\left(92 \right)} + \sin{\left(70 \right)} \cos{\left(70 \right)} + \sin{\left(48 \right)} \cos{\left(48 \right)} + \sin{\left(26 \right)} \cos{\left(26 \right)} + \sin{\left(4 \right)} \cos{\left(4 \right)} + \sin{\left(7 \right)} \cos{\left(7 \right)} + \sin{\left(29 \right)} \cos{\left(29 \right)} + \sin{\left(51 \right)} \cos{\left(51 \right)} + \sin{\left(73 \right)} \cos{\left(73 \right)} + \sin{\left(95 \right)} \cos{\left(95 \right)} + \sin{\left(117 \right)} \cos{\left(117 \right)} + \sin{\left(139 \right)} \cos{\left(139 \right)} + \sin{\left(161 \right)} \cos{\left(161 \right)}$$
cos(1)*sin(1) + cos(2)*sin(2) + cos(3)*sin(3) + cos(4)*sin(4) + cos(5)*sin(5) + cos(6)*sin(6) + cos(7)*sin(7) + cos(8)*sin(8) + cos(9)*sin(9) + cos(10)*sin(10) + cos(11)*sin(11) + cos(12)*sin(12) + cos(13)*sin(13) + cos(14)*sin(14) + cos(15)*sin(15) + cos(16)*sin(16) + cos(17)*sin(17) + cos(18)*sin(18) + cos(19)*sin(19) + cos(20)*sin(20) + cos(21)*sin(21) + cos(22)*sin(22) + cos(23)*sin(23) + cos(24)*sin(24) + cos(25)*sin(25) + cos(26)*sin(26) + cos(27)*sin(27) + cos(28)*sin(28) + cos(29)*sin(29) + cos(30)*sin(30) + cos(31)*sin(31) + cos(32)*sin(32) + cos(33)*sin(33) + cos(34)*sin(34) + cos(35)*sin(35) + cos(36)*sin(36) + cos(37)*sin(37) + cos(38)*sin(38) + cos(39)*sin(39) + cos(40)*sin(40) + cos(41)*sin(41) + cos(42)*sin(42) + cos(43)*sin(43) + cos(44)*sin(44) + cos(45)*sin(45) + cos(46)*sin(46) + cos(47)*sin(47) + cos(48)*sin(48) + cos(49)*sin(49) + cos(50)*sin(50) + cos(51)*sin(51) + cos(52)*sin(52) + cos(53)*sin(53) + cos(54)*sin(54) + cos(55)*sin(55) + cos(56)*sin(56) + cos(57)*sin(57) + cos(58)*sin(58) + cos(59)*sin(59) + cos(60)*sin(60) + cos(61)*sin(61) + cos(62)*sin(62) + cos(63)*sin(63) + cos(64)*sin(64) + cos(65)*sin(65) + cos(66)*sin(66) + cos(67)*sin(67) + cos(68)*sin(68) + cos(69)*sin(69) + cos(70)*sin(70) + cos(71)*sin(71) + cos(72)*sin(72) + cos(73)*sin(73) + cos(74)*sin(74) + cos(75)*sin(75) + cos(76)*sin(76) + cos(77)*sin(77) + cos(78)*sin(78) + cos(79)*sin(79) + cos(80)*sin(80) + cos(81)*sin(81) + cos(82)*sin(82) + cos(83)*sin(83) + cos(84)*sin(84) + cos(85)*sin(85) + cos(86)*sin(86) + cos(87)*sin(87) + cos(88)*sin(88) + cos(89)*sin(89) + cos(90)*sin(90) + cos(91)*sin(91) + cos(92)*sin(92) + cos(93)*sin(93) + cos(94)*sin(94) + cos(95)*sin(95) + cos(96)*sin(96) + cos(97)*sin(97) + cos(98)*sin(98) + cos(99)*sin(99) + cos(100)*sin(100) + cos(101)*sin(101) + cos(102)*sin(102) + cos(103)*sin(103) + cos(104)*sin(104) + cos(105)*sin(105) + cos(106)*sin(106) + cos(107)*sin(107) + cos(108)*sin(108) + cos(109)*sin(109) + cos(110)*sin(110) + cos(111)*sin(111) + cos(112)*sin(112) + cos(113)*sin(113) + cos(114)*sin(114) + cos(115)*sin(115) + cos(116)*sin(116) + cos(117)*sin(117) + cos(118)*sin(118) + cos(119)*sin(119) + cos(120)*sin(120) + cos(121)*sin(121) + cos(122)*sin(122) + cos(123)*sin(123) + cos(124)*sin(124) + cos(125)*sin(125) + cos(126)*sin(126) + cos(127)*sin(127) + cos(128)*sin(128) + cos(129)*sin(129) + cos(130)*sin(130) + cos(131)*sin(131) + cos(132)*sin(132) + cos(133)*sin(133) + cos(134)*sin(134) + cos(135)*sin(135) + cos(136)*sin(136) + cos(137)*sin(137) + cos(138)*sin(138) + cos(139)*sin(139) + cos(140)*sin(140) + cos(141)*sin(141) + cos(142)*sin(142) + cos(143)*sin(143) + cos(144)*sin(144) + cos(145)*sin(145) + cos(146)*sin(146) + cos(147)*sin(147) + cos(148)*sin(148) + cos(149)*sin(149) + cos(150)*sin(150) + cos(151)*sin(151) + cos(152)*sin(152) + cos(153)*sin(153) + cos(154)*sin(154) + cos(155)*sin(155) + cos(156)*sin(156) + cos(157)*sin(157) + cos(158)*sin(158) + cos(159)*sin(159) + cos(160)*sin(160) + cos(161)*sin(161) + cos(162)*sin(162) + cos(163)*sin(163) + cos(164)*sin(164) + cos(165)*sin(165) + cos(166)*sin(166) + cos(167)*sin(167) + cos(168)*sin(168) + cos(169)*sin(169) + cos(170)*sin(170) + cos(171)*sin(171) + cos(172)*sin(172) + cos(173)*sin(173) + cos(174)*sin(174) + cos(175)*sin(175) + cos(176)*sin(176) + cos(177)*sin(177) + cos(178)*sin(178) + cos(179)*sin(179) + cos(180)*sin(180)
Respuesta numérica [src]
0.445791073599621770319221372075
0.445791073599621770319221372075
Gráfico
Suma de la serie sinn*cosn

    Ejemplos de hallazgo de la suma de la serie