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sqrt(1-(2*n-1)/(2*n))

Suma de la serie sqrt(1-(2*n-1)/(2*n))



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Solución

Ha introducido [src]
  20                   
____                   
\   `                  
 \        _____________
  \      /     2*n - 1 
  /     /  1 - ------- 
 /    \/         2*n   
/___,                  
n = 1                  
$$\sum_{n=1}^{20} \sqrt{1 - \frac{2 n - 1}{2 n}}$$
Sum(sqrt(1 - (2*n - 1)/(2*n)), (n, 1, 20))
Velocidad de la convergencia de la serie
Respuesta [src]
       ___     ___     ___     ___     ____     ____     ____     ____     ____     ____       ____        ___
11   \/ 6    \/ 3    \/ 5    \/ 7    \/ 14    \/ 22    \/ 26    \/ 30    \/ 34    \/ 38    3*\/ 10    25*\/ 2 
-- + ----- + ----- + ----- + ----- + ------ + ------ + ------ + ------ + ------ + ------ + -------- + --------
12     4       6       10      14      14       22       26       30       34       38        20         24   
$$\frac{\sqrt{38}}{38} + \frac{\sqrt{34}}{34} + \frac{\sqrt{30}}{30} + \frac{\sqrt{7}}{14} + \frac{\sqrt{26}}{26} + \frac{\sqrt{22}}{22} + \frac{\sqrt{5}}{10} + \frac{\sqrt{14}}{14} + \frac{\sqrt{3}}{6} + \frac{3 \sqrt{10}}{20} + \frac{\sqrt{6}}{4} + \frac{11}{12} + \frac{25 \sqrt{2}}{24}$$
11/12 + sqrt(6)/4 + sqrt(3)/6 + sqrt(5)/10 + sqrt(7)/14 + sqrt(14)/14 + sqrt(22)/22 + sqrt(26)/26 + sqrt(30)/30 + sqrt(34)/34 + sqrt(38)/38 + 3*sqrt(10)/20 + 25*sqrt(2)/24
Respuesta numérica [src]
5.37065633322364316328960473872
5.37065633322364316328960473872
Gráfico
Suma de la serie sqrt(1-(2*n-1)/(2*n))

    Ejemplos de hallazgo de la suma de la serie