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Suma de la serie:
(-1)^n/n^3
1/n^5
i
n/n^2
Expresiones idénticas
ln^ dos (abs(uno +n))*cos(((n^ dos)+ uno)/ cien)
ln al cuadrado (abs(1 más n)) multiplicar por coseno de (((n al cuadrado ) más 1) dividir por 100)
ln en el grado dos (abs(uno más n)) multiplicar por coseno de (((n en el grado dos) más uno) dividir por cien)
ln2(abs(1+n))*cos(((n2)+1)/100)
ln2abs1+n*cosn2+1/100
ln²(abs(1+n))*cos(((n²)+1)/100)
ln en el grado 2(abs(1+n))*cos(((n en el grado 2)+1)/100)
ln^2(abs(1+n))cos(((n^2)+1)/100)
ln2(abs(1+n))cos(((n2)+1)/100)
ln2abs1+ncosn2+1/100
ln^2abs1+ncosn^2+1/100
ln^2(abs(1+n))*cos(((n^2)+1) dividir por 100)
Expresiones semejantes
ln^2(abs(1-n))*cos(((n^2)+1)/100)
ln^2(abs(1+n))*cos(((n^2)-1)/100)
Expresiones con funciones
ln
ln(n^2+1/8n^2+1)
ln(x+1)^n/n!
ln(n+1)/sqrt(n^5+5n^4+2)
ln(n^2+x^2)/(n*sqrt(n^2+x^2))
ln(sec(pi/n))
Coseno cos
cos^2(n+3)/sqrt(n^3+5)
cos(П/6(2n-1))
cos(т)
cos(x+n)
cos(x)+sin(x)-x

Suma de la serie/ ln^2(abs(1+n))*cos(((n^2)+1)/100)

Suma de la serie ln^2(abs(1+n))*cos(((n^2)+1)/100)

Solución

Ha introducido [src]

 100                           
____                           
\   `                          
 \                     / 2    \
  \      2             |n  + 1|
  /   log (|1 + n|)*cos|------|
 /                     \ 100  /
/___,                          
n = 1

\sum_{n=1}^{100} \log{\left(\left|{n + 1}\right| \right)}^{2} \cos{\left(\frac{n^{2} + 1}{100} \right)}

Sum(log(|1 + n|)^2*cos((n^2 + 1)/100), (n, 1, 100))

Velocidad de la convergencia de la serie

Respuesta [src]

   2                   2                   2                   2       / 17\      2       /13\      2       / 37\      2                  2       /13\      2        /41\      2        /101\      2        /61\      2        /29\      2        /17\      2        /197\      2        /113\      2        /257\      2        /29\      2                    2        /181\      2        /401\      2        /221\      2        /97\      2        /53\      2        /577\      2        /313\      2        /677\      2        /73\      2        /157\      2        /421\      2        /901\      2        /481\      2                    2        /109\      2        /1157\      2        /613\      2        /1297\      2        /137\      2        /289\      2        /761\      2        /1601\      2        /841\      2        /353\      2                    2        /1937\      2        /1013\      2        /2117\      2        /221\      2        /461\      2        /1201\      2        /2501\      2        /1301\      2        /541\      2        /281\      2        /2917\      2        /1513\      2        /3137\      2                    2        /673\      2        /1741\      2        /3601\      2        /1861\      2        /769\      2        /397\      2        /4097\      2        /2113\      2        /4357\      2        /449\      2                     2        /2381\      2        /4901\      2        /2521\      2        /1037\      2        /533\      2        /5477\      2        /2813\      2        /5777\      2        /593\      2        /1217\      2        /3121\      2        /6401\      2        /3281\      2                     2        /689\      2        /7057\      2        /3613\      2        /7397\      2        /757\      2        /1549\      2        /3961\      2        /8101\      2        /4141\      2        /1693\      2                     2        /8837\      2        /4513\      2        /9217\      2        /941\      2        /1921\      2         /4901\      2         /10001\
log (2)*cos(1/50) + log (3)*cos(1/20) + log (4)*cos(1/10) + log (5)*cos|---| + log (6)*cos|--| + log (7)*cos|---| + log (8)*cos(1/2) + log (9)*cos|--| + log (10)*cos|--| + log (11)*cos|---| + log (12)*cos|--| + log (13)*cos|--| + log (14)*cos|--| + log (15)*cos|---| + log (16)*cos|---| + log (17)*cos|---| + log (18)*cos|--| + log (19)*cos(13/4) + log (20)*cos|---| + log (21)*cos|---| + log (22)*cos|---| + log (23)*cos|--| + log (24)*cos|--| + log (25)*cos|---| + log (26)*cos|---| + log (27)*cos|---| + log (28)*cos|--| + log (29)*cos|---| + log (30)*cos|---| + log (31)*cos|---| + log (32)*cos|---| + log (33)*cos(41/4) + log (34)*cos|---| + log (35)*cos|----| + log (36)*cos|---| + log (37)*cos|----| + log (38)*cos|---| + log (39)*cos|---| + log (40)*cos|---| + log (41)*cos|----| + log (42)*cos|---| + log (43)*cos|---| + log (44)*cos(37/2) + log (45)*cos|----| + log (46)*cos|----| + log (47)*cos|----| + log (48)*cos|---| + log (49)*cos|---| + log (50)*cos|----| + log (51)*cos|----| + log (52)*cos|----| + log (53)*cos|---| + log (54)*cos|---| + log (55)*cos|----| + log (56)*cos|----| + log (57)*cos|----| + log (58)*cos(65/2) + log (59)*cos|---| + log (60)*cos|----| + log (61)*cos|----| + log (62)*cos|----| + log (63)*cos|---| + log (64)*cos|---| + log (65)*cos|----| + log (66)*cos|----| + log (67)*cos|----| + log (68)*cos|---| + log (69)*cos(185/4) + log (70)*cos|----| + log (71)*cos|----| + log (72)*cos|----| + log (73)*cos|----| + log (74)*cos|---| + log (75)*cos|----| + log (76)*cos|----| + log (77)*cos|----| + log (78)*cos|---| + log (79)*cos|----| + log (80)*cos|----| + log (81)*cos|----| + log (82)*cos|----| + log (83)*cos(269/4) + log (84)*cos|---| + log (85)*cos|----| + log (86)*cos|----| + log (87)*cos|----| + log (88)*cos|---| + log (89)*cos|----| + log (90)*cos|----| + log (91)*cos|----| + log (92)*cos|----| + log (93)*cos|----| + log (94)*cos(173/2) + log (95)*cos|----| + log (96)*cos|----| + log (97)*cos|----| + log (98)*cos|---| + log (99)*cos|----| + log (100)*cos|----| + log (101)*cos|-----|
                                                                       \100/              \50/              \100/                                 \20/               \50/               \100/               \50/               \20/               \10/               \100/               \ 50/               \100/               \10/                                    \ 50/               \100/               \ 50/               \20/               \10/               \100/               \ 50/               \100/               \10/               \ 20/               \ 50/               \100/               \ 50/                                    \ 10/               \100 /               \ 50/               \100 /               \ 10/               \ 20/               \ 50/               \100 /               \ 50/               \ 20/                                    \100 /               \ 50 /               \100 /               \ 10/               \ 20/               \ 50 /               \100 /               \ 50 /               \ 20/               \ 10/               \100 /               \ 50 /               \100 /                                    \ 20/               \ 50 /               \100 /               \ 50 /               \ 20/               \ 10/               \100 /               \ 50 /               \100 /               \ 10/                                     \ 50 /               \100 /               \ 50 /               \ 20 /               \ 10/               \100 /               \ 50 /               \100 /               \ 10/               \ 20 /               \ 50 /               \100 /               \ 50 /                                     \ 10/               \100 /               \ 50 /               \100 /               \ 10/               \ 20 /               \ 50 /               \100 /               \ 50 /               \ 20 /                                     \100 /               \ 50 /               \100 /               \ 10/               \ 20 /                \ 50 /                \ 100 /

\log{\left(93 \right)}^{2} \cos{\left(\frac{1693}{20} \right)} + \log{\left(86 \right)}^{2} \cos{\left(\frac{3613}{50} \right)} + \log{\left(74 \right)}^{2} \cos{\left(\frac{533}{10} \right)} + \log{\left(82 \right)}^{2} \cos{\left(\frac{3281}{50} \right)} + \log{\left(78 \right)}^{2} \cos{\left(\frac{593}{10} \right)} + \log{\left(65 \right)}^{2} \cos{\left(\frac{4097}{100} \right)} + \log{\left(100 \right)}^{2} \cos{\left(\frac{4901}{50} \right)} + \log{\left(60 \right)}^{2} \cos{\left(\frac{1741}{50} \right)} + \log{\left(70 \right)}^{2} \cos{\left(\frac{2381}{50} \right)} + \log{\left(90 \right)}^{2} \cos{\left(\frac{3961}{50} \right)} + \log{\left(54 \right)}^{2} \cos{\left(\frac{281}{10} \right)} + \log{\left(48 \right)}^{2} \cos{\left(\frac{221}{10} \right)} + \log{\left(96 \right)}^{2} \cos{\left(\frac{4513}{50} \right)} + \log{\left(41 \right)}^{2} \cos{\left(\frac{1601}{100} \right)} + \log{\left(40 \right)}^{2} \cos{\left(\frac{761}{50} \right)} + \log{\left(32 \right)}^{2} \cos{\left(\frac{481}{50} \right)} + \log{\left(69 \right)}^{2} \cos{\left(\frac{185}{4} \right)} + \log{\left(31 \right)}^{2} \cos{\left(\frac{901}{100} \right)} + \log{\left(59 \right)}^{2} \cos{\left(\frac{673}{20} \right)} + \log{\left(97 \right)}^{2} \cos{\left(\frac{9217}{100} \right)} + \log{\left(47 \right)}^{2} \cos{\left(\frac{2117}{100} \right)} + \log{\left(55 \right)}^{2} \cos{\left(\frac{2917}{100} \right)} + \log{\left(89 \right)}^{2} \cos{\left(\frac{1549}{20} \right)} + \log{\left(19 \right)}^{2} \cos{\left(\frac{13}{4} \right)} + \log{\left(33 \right)}^{2} \cos{\left(\frac{41}{4} \right)} + \log{\left(18 \right)}^{2} \cos{\left(\frac{29}{10} \right)} + \log{\left(20 \right)}^{2} \cos{\left(\frac{181}{50} \right)} + \log{\left(79 \right)}^{2} \cos{\left(\frac{1217}{20} \right)} + \log{\left(49 \right)}^{2} \cos{\left(\frac{461}{20} \right)} + \log{\left(64 \right)}^{2} \cos{\left(\frac{397}{10} \right)} + \log{\left(17 \right)}^{2} \cos{\left(\frac{257}{100} \right)} + \log{\left(30 \right)}^{2} \cos{\left(\frac{421}{50} \right)} + \log{\left(42 \right)}^{2} \cos{\left(\frac{841}{50} \right)} + \log{\left(21 \right)}^{2} \cos{\left(\frac{401}{100} \right)} + \log{\left(83 \right)}^{2} \cos{\left(\frac{269}{4} \right)} + \log{\left(53 \right)}^{2} \cos{\left(\frac{541}{20} \right)} + \log{\left(16 \right)}^{2} \cos{\left(\frac{113}{50} \right)} + \log{\left(99 \right)}^{2} \cos{\left(\frac{1921}{20} \right)} + \log{\left(39 \right)}^{2} \cos{\left(\frac{289}{20} \right)} + \log{\left(75 \right)}^{2} \cos{\left(\frac{5477}{100} \right)} + \log{\left(15 \right)}^{2} \cos{\left(\frac{197}{100} \right)} + \log{\left(22 \right)}^{2} \cos{\left(\frac{221}{50} \right)} + \log{\left(66 \right)}^{2} \cos{\left(\frac{2113}{50} \right)} + \log{\left(61 \right)}^{2} \cos{\left(\frac{3601}{100} \right)} + \log{\left(34 \right)}^{2} \cos{\left(\frac{109}{10} \right)} + \log{\left(14 \right)}^{2} \cos{\left(\frac{17}{10} \right)} + \log{\left(73 \right)}^{2} \cos{\left(\frac{1037}{20} \right)} + \log{\left(29 \right)}^{2} \cos{\left(\frac{157}{20} \right)} + \log{\left(2 \right)}^{2} \cos{\left(\frac{1}{50} \right)} + \log{\left(13 \right)}^{2} \cos{\left(\frac{29}{20} \right)} + \log{\left(3 \right)}^{2} \cos{\left(\frac{1}{20} \right)} + \log{\left(23 \right)}^{2} \cos{\left(\frac{97}{20} \right)} + \log{\left(4 \right)}^{2} \cos{\left(\frac{1}{10} \right)} + \log{\left(12 \right)}^{2} \cos{\left(\frac{61}{50} \right)} + \log{\left(94 \right)}^{2} \cos{\left(\frac{173}{2} \right)} + \log{\left(85 \right)}^{2} \cos{\left(\frac{7057}{100} \right)} + \log{\left(46 \right)}^{2} \cos{\left(\frac{1013}{50} \right)} + \log{\left(5 \right)}^{2} \cos{\left(\frac{17}{100} \right)} + \log{\left(87 \right)}^{2} \cos{\left(\frac{7397}{100} \right)} + \log{\left(11 \right)}^{2} \cos{\left(\frac{101}{100} \right)} + \log{\left(6 \right)}^{2} \cos{\left(\frac{13}{50} \right)} + \log{\left(7 \right)}^{2} \cos{\left(\frac{37}{100} \right)} + \log{\left(10 \right)}^{2} \cos{\left(\frac{41}{50} \right)} + \log{\left(8 \right)}^{2} \cos{\left(\frac{1}{2} \right)} + \log{\left(9 \right)}^{2} \cos{\left(\frac{13}{20} \right)} + \log{\left(43 \right)}^{2} \cos{\left(\frac{353}{20} \right)} + \log{\left(24 \right)}^{2} \cos{\left(\frac{53}{10} \right)} + \log{\left(38 \right)}^{2} \cos{\left(\frac{137}{10} \right)} + \log{\left(71 \right)}^{2} \cos{\left(\frac{4901}{100} \right)} + \log{\left(28 \right)}^{2} \cos{\left(\frac{73}{10} \right)} + \log{\left(77 \right)}^{2} \cos{\left(\frac{5777}{100} \right)} + \log{\left(56 \right)}^{2} \cos{\left(\frac{1513}{50} \right)} + \log{\left(50 \right)}^{2} \cos{\left(\frac{1201}{50} \right)} + \log{\left(35 \right)}^{2} \cos{\left(\frac{1157}{100} \right)} + \log{\left(81 \right)}^{2} \cos{\left(\frac{6401}{100} \right)} + \log{\left(58 \right)}^{2} \cos{\left(\frac{65}{2} \right)} + \log{\left(92 \right)}^{2} \cos{\left(\frac{4141}{50} \right)} + \log{\left(25 \right)}^{2} \cos{\left(\frac{577}{100} \right)} + \log{\left(27 \right)}^{2} \cos{\left(\frac{677}{100} \right)} + \log{\left(52 \right)}^{2} \cos{\left(\frac{1301}{50} \right)} + \log{\left(26 \right)}^{2} \cos{\left(\frac{313}{50} \right)} + \log{\left(68 \right)}^{2} \cos{\left(\frac{449}{10} \right)} + \log{\left(37 \right)}^{2} \cos{\left(\frac{1297}{100} \right)} + \log{\left(36 \right)}^{2} \cos{\left(\frac{613}{50} \right)} + \log{\left(63 \right)}^{2} \cos{\left(\frac{769}{20} \right)} + \log{\left(45 \right)}^{2} \cos{\left(\frac{1937}{100} \right)} + \log{\left(44 \right)}^{2} \cos{\left(\frac{37}{2} \right)} + \log{\left(62 \right)}^{2} \cos{\left(\frac{1861}{50} \right)} + \log{\left(51 \right)}^{2} \cos{\left(\frac{2501}{100} \right)} + \log{\left(91 \right)}^{2} \cos{\left(\frac{8101}{100} \right)} + \log{\left(67 \right)}^{2} \cos{\left(\frac{4357}{100} \right)} + \log{\left(57 \right)}^{2} \cos{\left(\frac{3137}{100} \right)} + \log{\left(80 \right)}^{2} \cos{\left(\frac{3121}{50} \right)} + \log{\left(76 \right)}^{2} \cos{\left(\frac{2813}{50} \right)} + \log{\left(72 \right)}^{2} \cos{\left(\frac{2521}{50} \right)} + \log{\left(101 \right)}^{2} \cos{\left(\frac{10001}{100} \right)} + \log{\left(95 \right)}^{2} \cos{\left(\frac{8837}{100} \right)} + \log{\left(88 \right)}^{2} \cos{\left(\frac{757}{10} \right)} + \log{\left(84 \right)}^{2} \cos{\left(\frac{689}{10} \right)} + \log{\left(98 \right)}^{2} \cos{\left(\frac{941}{10} \right)}

log(2)^2*cos(1/50) + log(3)^2*cos(1/20) + log(4)^2*cos(1/10) + log(5)^2*cos(17/100) + log(6)^2*cos(13/50) + log(7)^2*cos(37/100) + log(8)^2*cos(1/2) + log(9)^2*cos(13/20) + log(10)^2*cos(41/50) + log(11)^2*cos(101/100) + log(12)^2*cos(61/50) + log(13)^2*cos(29/20) + log(14)^2*cos(17/10) + log(15)^2*cos(197/100) + log(16)^2*cos(113/50) + log(17)^2*cos(257/100) + log(18)^2*cos(29/10) + log(19)^2*cos(13/4) + log(20)^2*cos(181/50) + log(21)^2*cos(401/100) + log(22)^2*cos(221/50) + log(23)^2*cos(97/20) + log(24)^2*cos(53/10) + log(25)^2*cos(577/100) + log(26)^2*cos(313/50) + log(27)^2*cos(677/100) + log(28)^2*cos(73/10) + log(29)^2*cos(157/20) + log(30)^2*cos(421/50) + log(31)^2*cos(901/100) + log(32)^2*cos(481/50) + log(33)^2*cos(41/4) + log(34)^2*cos(109/10) + log(35)^2*cos(1157/100) + log(36)^2*cos(613/50) + log(37)^2*cos(1297/100) + log(38)^2*cos(137/10) + log(39)^2*cos(289/20) + log(40)^2*cos(761/50) + log(41)^2*cos(1601/100) + log(42)^2*cos(841/50) + log(43)^2*cos(353/20) + log(44)^2*cos(37/2) + log(45)^2*cos(1937/100) + log(46)^2*cos(1013/50) + log(47)^2*cos(2117/100) + log(48)^2*cos(221/10) + log(49)^2*cos(461/20) + log(50)^2*cos(1201/50) + log(51)^2*cos(2501/100) + log(52)^2*cos(1301/50) + log(53)^2*cos(541/20) + log(54)^2*cos(281/10) + log(55)^2*cos(2917/100) + log(56)^2*cos(1513/50) + log(57)^2*cos(3137/100) + log(58)^2*cos(65/2) + log(59)^2*cos(673/20) + log(60)^2*cos(1741/50) + log(61)^2*cos(3601/100) + log(62)^2*cos(1861/50) + log(63)^2*cos(769/20) + log(64)^2*cos(397/10) + log(65)^2*cos(4097/100) + log(66)^2*cos(2113/50) + log(67)^2*cos(4357/100) + log(68)^2*cos(449/10) + log(69)^2*cos(185/4) + log(70)^2*cos(2381/50) + log(71)^2*cos(4901/100) + log(72)^2*cos(2521/50) + log(73)^2*cos(1037/20) + log(74)^2*cos(533/10) + log(75)^2*cos(5477/100) + log(76)^2*cos(2813/50) + log(77)^2*cos(5777/100) + log(78)^2*cos(593/10) + log(79)^2*cos(1217/20) + log(80)^2*cos(3121/50) + log(81)^2*cos(6401/100) + log(82)^2*cos(3281/50) + log(83)^2*cos(269/4) + log(84)^2*cos(689/10) + log(85)^2*cos(7057/100) + log(86)^2*cos(3613/50) + log(87)^2*cos(7397/100) + log(88)^2*cos(757/10) + log(89)^2*cos(1549/20) + log(90)^2*cos(3961/50) + log(91)^2*cos(8101/100) + log(92)^2*cos(4141/50) + log(93)^2*cos(1693/20) + log(94)^2*cos(173/2) + log(95)^2*cos(8837/100) + log(96)^2*cos(4513/50) + log(97)^2*cos(9217/100) + log(98)^2*cos(941/10) + log(99)^2*cos(1921/20) + log(100)^2*cos(4901/50) + log(101)^2*cos(10001/100)

Respuesta numérica [src]

9.41016900266547420349336243811

9.41016900266547420349336243811

Gráfico

Suma de la serie ln^2(abs(1+n))*cos(((n^2)+1)/100)

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 ln^2(abs(1+n))*cos(((n^2)+1)/100)

Solución

Ejemplos de hallazgo de la suma de la serie