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cos(pi*n/100)/29

Suma de la serie cos(pi*n/100)/29



=

Solución

Ha introducido [src]
  80           
____           
\   `          
 \       /pi*n\
  \   cos|----|
   )     \100 /
  /   ---------
 /        29   
/___,          
n = 1          
$$\sum_{n=1}^{80} \frac{\cos{\left(\frac{\pi n}{100} \right)}}{29}$$
Sum(cos((pi*n)/100)/29, (n, 1, 80))
Velocidad de la convergencia de la serie
Respuesta [src]
     ___________                                                                                                                                                                                                                                 ___________              ___________                    
    /       ___                                                                                                                                                                                                         /      ___\             /       ___              /       ___          /      ___\
   /  5   \/ 5        /pi\      /pi\      / pi\      /2*pi\      /3*pi\      /3*pi\      /3*pi\      /4*pi\      /7*pi\      /7*pi\      /9*pi\      /9*pi\      /11*pi\      /13*pi\      /17*pi\      /19*pi\     ___ |1   \/ 5 |     ___    /  5   \/ 5       ___    /  5   \/ 5       ___ |1   \/ 5 |
  /   - + -----    cos|--|   cos|--|   cos|---|   cos|----|   cos|----|   cos|----|   cos|----|   cos|----|   cos|----|   cos|----|   cos|----|   cos|----|   cos|-----|   cos|-----|   cos|-----|   cos|-----|   \/ 2 *|- - -----|   \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    \/ 2 *|- + -----|
\/    8     8         \25/      \50/      \100/      \ 25 /      \ 25 /      \ 50 /      \100 /      \ 25 /      \ 50 /      \100 /      \ 50 /      \100 /      \ 100 /      \ 100 /      \ 100 /      \ 100 /         \4     4  /         \/    8     8            \/    8     8            \4     4  /
---------------- + ------- + ------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + ---------- + ---------- + ---------- + ---------- - ----------------- + ---------------------- + ---------------------- + -----------------
       29             29        29        29          29          29          29          29          29          29          29          29          29          29           29           29           29               58                    58                       58                     58       
$$- \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{58} + \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{58} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{58} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{58} + \frac{\cos{\left(\frac{19 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{9 \pi}{50} \right)}}{29} + \frac{\cos{\left(\frac{17 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{4 \pi}{25} \right)}}{29} + \frac{\cos{\left(\frac{7 \pi}{50} \right)}}{29} + \frac{\cos{\left(\frac{13 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{3 \pi}{25} \right)}}{29} + \frac{\cos{\left(\frac{11 \pi}{100} \right)}}{29} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{29} + \frac{\cos{\left(\frac{9 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{2 \pi}{25} \right)}}{29} + \frac{\cos{\left(\frac{7 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{3 \pi}{50} \right)}}{29} + \frac{\cos{\left(\frac{\pi}{25} \right)}}{29} + \frac{\cos{\left(\frac{3 \pi}{100} \right)}}{29} + \frac{\cos{\left(\frac{\pi}{50} \right)}}{29} + \frac{\cos{\left(\frac{\pi}{100} \right)}}{29}$$
sqrt(5/8 + sqrt(5)/8)/29 + cos(pi/25)/29 + cos(pi/50)/29 + cos(pi/100)/29 + cos(2*pi/25)/29 + cos(3*pi/25)/29 + cos(3*pi/50)/29 + cos(3*pi/100)/29 + cos(4*pi/25)/29 + cos(7*pi/50)/29 + cos(7*pi/100)/29 + cos(9*pi/50)/29 + cos(9*pi/100)/29 + cos(11*pi/100)/29 + cos(13*pi/100)/29 + cos(17*pi/100)/29 + cos(19*pi/100)/29 - sqrt(2)*(1/4 - sqrt(5)/4)/58 + sqrt(2)*sqrt(5/8 - sqrt(5)/8)/58 + sqrt(2)*sqrt(5/8 + sqrt(5)/8)/58 + sqrt(2)*(1/4 + sqrt(5)/4)/58
Respuesta numérica [src]
0.613922011554485933366742033017
0.613922011554485933366742033017
Gráfico
Suma de la serie cos(pi*n/100)/29

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