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



=

Solución

Ha introducido [src]
  20                     
_____                    
\    `                   
 \         ______________
  \       /            n 
   \     /  1 + -2*n + - 
   /   \/              2 
  /    ------------------
 /             20        
/____,                   
n = 1                    
$$\sum_{n=1}^{20} \frac{\sqrt{\left(- 2 n + \frac{n}{2}\right) + 1}}{20}$$
Sum(sqrt(1 - 2*n + n/2)/20, (n, 1, 20))
Respuesta [src]
    ____       ____       ____       ____       ____       ____       ____       ____       _____         ___         ____         ____          ___
I*\/ 11    I*\/ 17    I*\/ 23    I*\/ 29    I*\/ 38    I*\/ 62    I*\/ 74    I*\/ 86    I*\/ 110    3*I*\/ 5    3*I*\/ 14    3*I*\/ 26    19*I*\/ 2 
-------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + --------- + --------- + ---------- + ---------- + ----------
   20         20         20         20         40         40         40         40          40          20          40           40           40    
$$\frac{\sqrt{38} i}{40} + \frac{\sqrt{11} i}{20} + \frac{\sqrt{62} i}{40} + \frac{\sqrt{17} i}{20} + \frac{\sqrt{74} i}{40} + \frac{\sqrt{86} i}{40} + \frac{\sqrt{23} i}{20} + \frac{\sqrt{110} i}{40} + \frac{\sqrt{29} i}{20} + \frac{3 \sqrt{14} i}{40} + \frac{3 \sqrt{5} i}{20} + \frac{3 \sqrt{26} i}{40} + \frac{19 \sqrt{2} i}{40}$$
i*sqrt(11)/20 + i*sqrt(17)/20 + i*sqrt(23)/20 + i*sqrt(29)/20 + i*sqrt(38)/40 + i*sqrt(62)/40 + i*sqrt(74)/40 + i*sqrt(86)/40 + i*sqrt(110)/40 + 3*i*sqrt(5)/20 + 3*i*sqrt(14)/40 + 3*i*sqrt(26)/40 + 19*i*sqrt(2)/40
Respuesta numérica [src]
3.61131009663122310400469200423*i
3.61131009663122310400469200423*i

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