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



=

Solución

Ha introducido [src]
  20                      
_____                     
\    `                    
 \         _______________
  \       /     2*n - 1   
   \     /  1 - -------*n 
   /   \/          2      
  /    -------------------
 /              20        
/____,                    
n = 1                     
$$\sum_{n=1}^{20} \frac{\sqrt{- n \frac{2 n - 1}{2} + 1}}{20}$$
Sum(sqrt(1 - (2*n - 1)/2*n)/20, (n, 1, 20))
Respuesta [src]
  ___       ___       ____       ____       ____       ____       _____       _____       _____       _____       ____       ____       _____       _____       _____       _____       _____       ______       ______
\/ 2    I*\/ 2    I*\/ 47    I*\/ 13    I*\/ 59    I*\/ 94    I*\/ 137    I*\/ 247    I*\/ 314    I*\/ 389    I*\/ 26    I*\/ 86    I*\/ 178    I*\/ 302    I*\/ 458    I*\/ 646    I*\/ 866    I*\/ 1118    I*\/ 1402 
----- + ------- + -------- + -------- + -------- + -------- + --------- + --------- + --------- + --------- + -------- + -------- + --------- + --------- + --------- + --------- + --------- + ---------- + ----------
  40       4         10         20         20         20          20          20          20          20         40         40          40          40          40          40          40          40           40    
$$\frac{\sqrt{2}}{40} + \frac{\sqrt{26} i}{40} + \frac{\sqrt{13} i}{20} + \frac{\sqrt{86} i}{40} + \frac{\sqrt{178} i}{40} + \frac{\sqrt{2} i}{4} + \frac{\sqrt{59} i}{20} + \frac{\sqrt{302} i}{40} + \frac{\sqrt{94} i}{20} + \frac{\sqrt{458} i}{40} + \frac{\sqrt{137} i}{20} + \frac{\sqrt{646} i}{40} + \frac{\sqrt{47} i}{10} + \frac{\sqrt{866} i}{40} + \frac{\sqrt{247} i}{20} + \frac{\sqrt{1118} i}{40} + \frac{\sqrt{314} i}{20} + \frac{\sqrt{1402} i}{40} + \frac{\sqrt{389} i}{20}$$
sqrt(2)/40 + i*sqrt(2)/4 + i*sqrt(47)/10 + i*sqrt(13)/20 + i*sqrt(59)/20 + i*sqrt(94)/20 + i*sqrt(137)/20 + i*sqrt(247)/20 + i*sqrt(314)/20 + i*sqrt(389)/20 + i*sqrt(26)/40 + i*sqrt(86)/40 + i*sqrt(178)/40 + i*sqrt(302)/40 + i*sqrt(458)/40 + i*sqrt(646)/40 + i*sqrt(866)/40 + i*sqrt(1118)/40 + i*sqrt(1402)/40
Respuesta numérica [src]
0.0353553390593273762200422181052 + 10.1368645006252603571876210518*i
0.0353553390593273762200422181052 + 10.1368645006252603571876210518*i

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