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sqrt(1-(2*n-1)/(2*n))*1/20

Suma de la serie sqrt(1-(2*n-1)/(2*n))*1/20



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Solución

Ha introducido [src]
  20                    
_____                   
\    `                  
 \         _____________
  \       /     2*n - 1 
   \     /  1 - ------- 
   /   \/         2*n   
  /    -----------------
 /             20       
/____,                  
n = 1                   
$$\sum_{n=1}^{20} \frac{\sqrt{1 - \frac{2 n - 1}{2 n}}}{20}$$
Sum(sqrt(1 - (2*n - 1)/(2*n))/20, (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    5*\/ 2 
--- + ----- + ----- + ----- + ----- + ------ + ------ + ------ + ------ + ------ + ------ + -------- + -------
240     80     120     200     280     280      440      520      600      680      760       400         96  
$$\frac{\sqrt{38}}{760} + \frac{\sqrt{34}}{680} + \frac{\sqrt{30}}{600} + \frac{\sqrt{7}}{280} + \frac{\sqrt{26}}{520} + \frac{\sqrt{22}}{440} + \frac{\sqrt{5}}{200} + \frac{\sqrt{14}}{280} + \frac{\sqrt{3}}{120} + \frac{3 \sqrt{10}}{400} + \frac{\sqrt{6}}{80} + \frac{11}{240} + \frac{5 \sqrt{2}}{96}$$
11/240 + sqrt(6)/80 + sqrt(3)/120 + sqrt(5)/200 + sqrt(7)/280 + sqrt(14)/280 + sqrt(22)/440 + sqrt(26)/520 + sqrt(30)/600 + sqrt(34)/680 + sqrt(38)/760 + 3*sqrt(10)/400 + 5*sqrt(2)/96
Respuesta numérica [src]
0.268532816661182158164480236936
0.268532816661182158164480236936
Gráfico
Suma de la serie sqrt(1-(2*n-1)/(2*n))*1/20

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