Sr Examen
Otras calculadoras
- Serie de Taylor paso a paso
- Serie de Fourier paso a paso
- Ecuaciones diferenciales paso a paso
- Producto de la serie
-
¿Cómo usar?
- Suma de la serie:
-
i
-
n^n/3^n*n!
-
(8/9)^n
-
8^n
-
Expresiones idénticas
- (- uno)^(n)*ln(n)/n
- ( menos 1) en el grado (n) multiplicar por ln(n) dividir por n
- ( menos uno) en el grado (n) multiplicar por ln(n) dividir por n
- (-1)(n)*ln(n)/n
- -1n*lnn/n
- (-1)^(n)ln(n)/n
- (-1)(n)ln(n)/n
- -1nlnn/n
- -1^nlnn/n
- (-1)^(n)*ln(n) dividir por n
-
Expresiones semejantes
- (1)^(n)*ln(n)/n
- (-1^n)lnn/n
- (-1)^n*ln(n)/(n^5+2)^(1/3)
- ((-1)^n)*ln(n)/n
- ((-1)^n*ln(n))/n*sqrt(n)
- ((-1)^n)*ln(n)/n^(1/2)
-
Expresiones con funciones
- ln
- ln^2(abs(1+n))*cos(((n^2)+1)/100)
- ln^2n(1,7)
- ln(n^2+x^2)/n^2
- ln^5(n)/(n^3+1)^1/2
- ln(n+2)/(2*ln(n)+1)
Suma de la serie (-1)^(n)*ln(n)/n
Solución
Ha introducido
[src]
100 ____ \ ` \ n \ (-1) *log(n) / ------------ / n /___, n = 1
$$\sum_{n=1}^{100} \frac{\left(-1\right)^{n} \log{\left(n \right)}}{n}$$
Sum(((-1)^n*log(n))/n, (n, 1, 100))
Velocidad de la convergencia de la serie
Respuesta
[src]
log(2) log(3) log(5) log(7) log(9) log(11) log(13) log(15) log(17) log(19) log(21) log(23) log(25) log(27) log(29) log(31) log(33) log(35) log(37) log(39) log(41) log(43) log(45) log(47) log(49) log(51) log(53) log(55) log(57) log(59) log(61) log(63) log(65) log(67) log(69) log(71) log(73) log(75) log(77) log(79) log(81) log(83) log(85) log(87) log(89) log(91) log(93) log(95) log(97) log(99) log(4) log(6) log(8) log(10) log(12) log(14) log(16) log(18) log(20) log(22) log(24) log(26) log(28) log(30) log(32) log(34) log(36) log(38) log(40) log(42) log(44) log(46) log(48) log(50) log(52) log(54) log(56) log(58) log(60) log(62) log(64) log(66) log(68) log(70) log(72) log(74) log(76) log(78) log(80) log(82) log(84) log(86) log(88) log(90) log(92) log(94) log(96) log(98) log(100) ------ - ------ - ------ - ------ - ------ - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- - ------- + ------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + -------- 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
$$- \frac{\log{\left(3 \right)}}{3} - \frac{\log{\left(5 \right)}}{5} - \frac{\log{\left(7 \right)}}{7} - \frac{\log{\left(9 \right)}}{9} - \frac{\log{\left(11 \right)}}{11} - \frac{\log{\left(13 \right)}}{13} - \frac{\log{\left(15 \right)}}{15} - \frac{\log{\left(17 \right)}}{17} - \frac{\log{\left(19 \right)}}{19} - \frac{\log{\left(21 \right)}}{21} - \frac{\log{\left(23 \right)}}{23} - \frac{\log{\left(25 \right)}}{25} - \frac{\log{\left(27 \right)}}{27} - \frac{\log{\left(29 \right)}}{29} - \frac{\log{\left(31 \right)}}{31} - \frac{\log{\left(33 \right)}}{33} - \frac{\log{\left(35 \right)}}{35} - \frac{\log{\left(37 \right)}}{37} - \frac{\log{\left(39 \right)}}{39} - \frac{\log{\left(41 \right)}}{41} - \frac{\log{\left(43 \right)}}{43} - \frac{\log{\left(45 \right)}}{45} - \frac{\log{\left(47 \right)}}{47} - \frac{\log{\left(49 \right)}}{49} - \frac{\log{\left(51 \right)}}{51} - \frac{\log{\left(53 \right)}}{53} - \frac{\log{\left(55 \right)}}{55} - \frac{\log{\left(57 \right)}}{57} - \frac{\log{\left(59 \right)}}{59} - \frac{\log{\left(61 \right)}}{61} - \frac{\log{\left(63 \right)}}{63} - \frac{\log{\left(65 \right)}}{65} - \frac{\log{\left(67 \right)}}{67} - \frac{\log{\left(69 \right)}}{69} - \frac{\log{\left(71 \right)}}{71} - \frac{\log{\left(73 \right)}}{73} - \frac{\log{\left(75 \right)}}{75} - \frac{\log{\left(77 \right)}}{77} - \frac{\log{\left(79 \right)}}{79} - \frac{\log{\left(81 \right)}}{81} - \frac{\log{\left(83 \right)}}{83} - \frac{\log{\left(85 \right)}}{85} - \frac{\log{\left(87 \right)}}{87} - \frac{\log{\left(89 \right)}}{89} - \frac{\log{\left(91 \right)}}{91} - \frac{\log{\left(93 \right)}}{93} - \frac{\log{\left(95 \right)}}{95} - \frac{\log{\left(97 \right)}}{97} - \frac{\log{\left(99 \right)}}{99} + \frac{\log{\left(100 \right)}}{100} + \frac{\log{\left(98 \right)}}{98} + \frac{\log{\left(96 \right)}}{96} + \frac{\log{\left(94 \right)}}{94} + \frac{\log{\left(92 \right)}}{92} + \frac{\log{\left(90 \right)}}{90} + \frac{\log{\left(88 \right)}}{88} + \frac{\log{\left(86 \right)}}{86} + \frac{\log{\left(84 \right)}}{84} + \frac{\log{\left(82 \right)}}{82} + \frac{\log{\left(80 \right)}}{80} + \frac{\log{\left(78 \right)}}{78} + \frac{\log{\left(76 \right)}}{76} + \frac{\log{\left(74 \right)}}{74} + \frac{\log{\left(72 \right)}}{72} + \frac{\log{\left(70 \right)}}{70} + \frac{\log{\left(68 \right)}}{68} + \frac{\log{\left(66 \right)}}{66} + \frac{\log{\left(64 \right)}}{64} + \frac{\log{\left(62 \right)}}{62} + \frac{\log{\left(60 \right)}}{60} + \frac{\log{\left(58 \right)}}{58} + \frac{\log{\left(56 \right)}}{56} + \frac{\log{\left(54 \right)}}{54} + \frac{\log{\left(52 \right)}}{52} + \frac{\log{\left(50 \right)}}{50} + \frac{\log{\left(48 \right)}}{48} + \frac{\log{\left(46 \right)}}{46} + \frac{\log{\left(44 \right)}}{44} + \frac{\log{\left(42 \right)}}{42} + \frac{\log{\left(40 \right)}}{40} + \frac{\log{\left(38 \right)}}{38} + \frac{\log{\left(36 \right)}}{36} + \frac{\log{\left(34 \right)}}{34} + \frac{\log{\left(32 \right)}}{32} + \frac{\log{\left(30 \right)}}{30} + \frac{\log{\left(28 \right)}}{28} + \frac{\log{\left(26 \right)}}{26} + \frac{\log{\left(24 \right)}}{24} + \frac{\log{\left(22 \right)}}{22} + \frac{\log{\left(20 \right)}}{20} + \frac{\log{\left(18 \right)}}{18} + \frac{\log{\left(16 \right)}}{16} + \frac{\log{\left(14 \right)}}{14} + \frac{\log{\left(12 \right)}}{12} + \frac{\log{\left(10 \right)}}{10} + \frac{\log{\left(8 \right)}}{8} + \frac{\log{\left(6 \right)}}{6} + \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(4 \right)}}{4}$$
log(2)/2 - log(3)/3 - log(5)/5 - log(7)/7 - log(9)/9 - log(11)/11 - log(13)/13 - log(15)/15 - log(17)/17 - log(19)/19 - log(21)/21 - log(23)/23 - log(25)/25 - log(27)/27 - log(29)/29 - log(31)/31 - log(33)/33 - log(35)/35 - log(37)/37 - log(39)/39 - log(41)/41 - log(43)/43 - log(45)/45 - log(47)/47 - log(49)/49 - log(51)/51 - log(53)/53 - log(55)/55 - log(57)/57 - log(59)/59 - log(61)/61 - log(63)/63 - log(65)/65 - log(67)/67 - log(69)/69 - log(71)/71 - log(73)/73 - log(75)/75 - log(77)/77 - log(79)/79 - log(81)/81 - log(83)/83 - log(85)/85 - log(87)/87 - log(89)/89 - log(91)/91 - log(93)/93 - log(95)/95 - log(97)/97 - log(99)/99 + log(4)/4 + log(6)/6 + log(8)/8 + log(10)/10 + log(12)/12 + log(14)/14 + log(16)/16 + log(18)/18 + log(20)/20 + log(22)/22 + log(24)/24 + log(26)/26 + log(28)/28 + log(30)/30 + log(32)/32 + log(34)/34 + log(36)/36 + log(38)/38 + log(40)/40 + log(42)/42 + log(44)/44 + log(46)/46 + log(48)/48 + log(50)/50 + log(52)/52 + log(54)/54 + log(56)/56 + log(58)/58 + log(60)/60 + log(62)/62 + log(64)/64 + log(66)/66 + log(68)/68 + log(70)/70 + log(72)/72 + log(74)/74 + log(76)/76 + log(78)/78 + log(80)/80 + log(82)/82 + log(84)/84 + log(86)/86 + log(88)/88 + log(90)/90 + log(92)/92 + log(94)/94 + log(96)/96 + log(98)/98 + log(100)/100
Gráfico
Ejemplos de hallazgo de la suma de la serie
- Suma de la serie de potencias
x^n/n
(x-1)^n
- Factorial
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
- Serie de Flint Hills
csc(n)^2/n^3
- Serie de cuadrados inversos
1/n^2
1/n^4
1/n^6
- Serie armónica
1/n
- Serie de Grandi
(-1)^n
- Serie alternada
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
- Serie de Newton-Mercator
(-1)^(n + 1)/n*x^n
- Investigar la convergencia de la serie
(3*n - 1)/(-5)^n