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cos(pi*n/100)/20/30

  • ¿Cómo usar?

  • Suma de la serie:
  • 3^n 3^n
  • i i
  • n^n/3^n*n! n^n/3^n*n!
  • n^3 n^3

  • Expresiones idénticas

  • cos(pi*n/ cien)/ veinte / treinta
  • coseno de ( número pi multiplicar por n dividir por 100) dividir por 20 dividir por 30
  • coseno de ( número pi multiplicar por n dividir por cien) dividir por veinte dividir por treinta
  • cos(pin/100)/20/30
  • cospin/100/20/30
  • cos(pi*n dividir por 100) dividir por 20 dividir por 30

  • Expresiones con funciones

  • Coseno cos
  • cos(т)
  • cos(x+n)
  • cos2^(n)/(2^n)
  • cos(x)+sin(x)-x
  • cos(pi/(4*n))/(2*n^3-1)^(1/5)
Suma de la serie/ cos(pi*n/100)/20/30

Suma de la serie cos(pi*n/100)/20/30


∑
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Solución

Ha introducido [src] 
  80              
_____             
\    `            
 \     /   /pi*n\\
  \    |cos|----||
   \   |   \100 /|
    )  |---------|
   /   \    20   /
  /    -----------
 /          30    
/____,            
n = 1
$$\sum_{n=1}^{80} \frac{\frac{1}{20} \cos{\left(\frac{\pi n}{100} \right)}}{30}$$ 
Sum((cos((pi*n)/100)/20)/30, (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  /
---------------- + ------- + ------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + ---------- + ---------- + ---------- + ---------- - ----------------- + ---------------------- + ---------------------- + -----------------
      600            600       600       600         600         600         600         600         600         600         600         600         600         600          600          600          600              1200                  1200                     1200                   1200
$$- \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{1200} + \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{1200} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{1200} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{1200} + \frac{\cos{\left(\frac{19 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{9 \pi}{50} \right)}}{600} + \frac{\cos{\left(\frac{17 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{4 \pi}{25} \right)}}{600} + \frac{\cos{\left(\frac{7 \pi}{50} \right)}}{600} + \frac{\cos{\left(\frac{13 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{3 \pi}{25} \right)}}{600} + \frac{\cos{\left(\frac{11 \pi}{100} \right)}}{600} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{600} + \frac{\cos{\left(\frac{9 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{2 \pi}{25} \right)}}{600} + \frac{\cos{\left(\frac{7 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{3 \pi}{50} \right)}}{600} + \frac{\cos{\left(\frac{\pi}{25} \right)}}{600} + \frac{\cos{\left(\frac{3 \pi}{100} \right)}}{600} + \frac{\cos{\left(\frac{\pi}{50} \right)}}{600} + \frac{\cos{\left(\frac{\pi}{100} \right)}}{600}$$ 
sqrt(5/8 + sqrt(5)/8)/600 + cos(pi/25)/600 + cos(pi/50)/600 + cos(pi/100)/600 + cos(2*pi/25)/600 + cos(3*pi/25)/600 + cos(3*pi/50)/600 + cos(3*pi/100)/600 + cos(4*pi/25)/600 + cos(7*pi/50)/600 + cos(7*pi/100)/600 + cos(9*pi/50)/600 + cos(9*pi/100)/600 + cos(11*pi/100)/600 + cos(13*pi/100)/600 + cos(17*pi/100)/600 + cos(19*pi/100)/600 - sqrt(2)*(1/4 - sqrt(5)/4)/1200 + sqrt(2)*sqrt(5/8 - sqrt(5)/8)/1200 + sqrt(2)*sqrt(5/8 + sqrt(5)/8)/1200 + sqrt(2)*(1/4 + sqrt(5)/4)/1200
Respuesta numérica [src] 
0.0296728972251334867793925315958
0.0296728972251334867793925315958
Gráfico
Suma de la serie cos(pi*n/100)/20/30

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