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Suma de la serie:
3^n
i
n^n/3^n*n!
n^3
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×x/n+3

Suma de la serie/ (-1)^(n)*ln(n)/n

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

Respuesta numérica [src]

0.182804628881937546588952657589

0.182804628881937546588952657589

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
```

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Suma de la serie (-1)^(n)*ln(n)/n

Solución

Ejemplos de hallazgo de la suma de la serie