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Suma de la serie:
(n/(2*n+1))^n
((2n+1)/((n+1)^3))*x^n
(5^n+2^n)/10^n
(2/7)^n
Expresiones idénticas
sqrt(uno + cero , ciento setenta y cuatro *(i+ cero , cinco))
raíz cuadrada de (1 más 0,174 multiplicar por (i más 0,5))
raíz cuadrada de (uno más cero , ciento setenta y cuatro multiplicar por (i más cero , cinco))
√(1+0,174*(i+0,5))
sqrt(1+0,174(i+0,5))
sqrt1+0,174i+0,5
Expresiones semejantes
sqrt(1+0,174*(i-0,5))
sqrt(1-0,174*(i+0,5))
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(9)*3
sqrt(n)/(n+3)
sqrt(1/n)-sqrt(log(1+1/n))
sqrt(2i)
sqrt(1+5n/n)

Suma de la serie/ sqrt(1+0,174*(i+0,5))

Suma de la serie sqrt(1+0,174*(i+0,5))

Solución

Ha introducido [src]

  45                        
____                        
\   `                       
 \        __________________
  \      /     87*(i + 1/2) 
  /     /  1 + ------------ 
 /    \/           500      
/___,                       
i = 0

\sum_{i=0}^{45} \sqrt{\frac{87 \left(i + \frac{1}{2}\right)}{500} + 1}

Sum(sqrt(1 + 87*(i + 1/2)/500), (i, 0, 45))

Velocidad de la convergencia de la serie

Respuesta [src]

  _____     _____     ______     ______     ______     ______     ______     ______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______       _____        ____
\/ 574    \/ 922    \/ 1270    \/ 1618    \/ 1966    \/ 2314    \/ 3010    \/ 3358    \/ 10870    \/ 12610    \/ 16090    \/ 17830    \/ 19570    \/ 21310    \/ 24790    \/ 26530    \/ 28270    \/ 30010    \/ 33490    \/ 35230    \/ 36970    \/ 42190    \/ 43930    \/ 45670    \/ 47410    \/ 50890    \/ 52630    \/ 54370    \/ 56110    \/ 59590    \/ 61330    \/ 63070    \/ 64810    \/ 68290    \/ 70030    \/ 71770    \/ 73510    \/ 76990    \/ 78730    \/ 80470    \/ 82210    \/ 85690    \/ 87430    \/ 89170    7*\/ 790    11*\/ 22 
------- + ------- + -------- + -------- + -------- + -------- + -------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + ---------
   20        20        20         20         20         20         20         20         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100          20

\frac{\sqrt{10870}}{100} + \frac{\sqrt{12610}}{100} + \frac{\sqrt{574}}{20} + \frac{\sqrt{16090}}{100} + \frac{\sqrt{17830}}{100} + \frac{\sqrt{19570}}{100} + \frac{\sqrt{21310}}{100} + \frac{\sqrt{922}}{20} + \frac{\sqrt{24790}}{100} + \frac{\sqrt{26530}}{100} + \frac{\sqrt{28270}}{100} + \frac{\sqrt{30010}}{100} + \frac{\sqrt{1270}}{20} + \frac{\sqrt{33490}}{100} + \frac{\sqrt{35230}}{100} + \frac{\sqrt{36970}}{100} + \frac{7 \sqrt{790}}{100} + \frac{\sqrt{1618}}{20} + \frac{\sqrt{42190}}{100} + \frac{\sqrt{43930}}{100} + \frac{\sqrt{45670}}{100} + \frac{\sqrt{47410}}{100} + \frac{\sqrt{1966}}{20} + \frac{\sqrt{50890}}{100} + \frac{\sqrt{52630}}{100} + \frac{\sqrt{54370}}{100} + \frac{\sqrt{56110}}{100} + \frac{\sqrt{2314}}{20} + \frac{\sqrt{59590}}{100} + \frac{\sqrt{61330}}{100} + \frac{\sqrt{63070}}{100} + \frac{\sqrt{64810}}{100} + \frac{11 \sqrt{22}}{20} + \frac{\sqrt{68290}}{100} + \frac{\sqrt{70030}}{100} + \frac{\sqrt{71770}}{100} + \frac{\sqrt{73510}}{100} + \frac{\sqrt{3010}}{20} + \frac{\sqrt{76990}}{100} + \frac{\sqrt{78730}}{100} + \frac{\sqrt{80470}}{100} + \frac{\sqrt{82210}}{100} + \frac{\sqrt{3358}}{20} + \frac{\sqrt{85690}}{100} + \frac{\sqrt{87430}}{100} + \frac{\sqrt{89170}}{100}

sqrt(574)/20 + sqrt(922)/20 + sqrt(1270)/20 + sqrt(1618)/20 + sqrt(1966)/20 + sqrt(2314)/20 + sqrt(3010)/20 + sqrt(3358)/20 + sqrt(10870)/100 + sqrt(12610)/100 + sqrt(16090)/100 + sqrt(17830)/100 + sqrt(19570)/100 + sqrt(21310)/100 + sqrt(24790)/100 + sqrt(26530)/100 + sqrt(28270)/100 + sqrt(30010)/100 + sqrt(33490)/100 + sqrt(35230)/100 + sqrt(36970)/100 + sqrt(42190)/100 + sqrt(43930)/100 + sqrt(45670)/100 + sqrt(47410)/100 + sqrt(50890)/100 + sqrt(52630)/100 + sqrt(54370)/100 + sqrt(56110)/100 + sqrt(59590)/100 + sqrt(61330)/100 + sqrt(63070)/100 + sqrt(64810)/100 + sqrt(68290)/100 + sqrt(70030)/100 + sqrt(71770)/100 + sqrt(73510)/100 + sqrt(76990)/100 + sqrt(78730)/100 + sqrt(80470)/100 + sqrt(82210)/100 + sqrt(85690)/100 + sqrt(87430)/100 + sqrt(89170)/100 + 7*sqrt(790)/100 + 11*sqrt(22)/20

Respuesta numérica [src]

99.6882459776836715116486075306

99.6882459776836715116486075306

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 sqrt(1+0,174*(i+0,5))

Solución

Ejemplos de hallazgo de la suma de la serie